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This paper considers linear panel data models with a grouped pattern of heterogeneity when the latent group membership structure and/or the values of slope coefficients change at a break point. We propose a least squares approach to jointly estimate the break point, group membership structure, and coefficients. The proposed estimators are consistent, and the asymptotic distribution of the coefficient estimators is identical to that under known break point and group structure even when the cross-sectional sample size is much larger than the length of time series. Monte Carlo simulations and an empirical example illustrate the use of the approach and associated inference.

To prevent mistakes in psychological assessment, the precision of test norms is important. This can be achieved by drawing a large normative sample and using regression-based norming. Based on that norming method, a procedure for sample size planning to make inference on Z-scores and percentile rank scores is proposed. Sampling variance formulas for these norm statistics are derived and used to obtain the optimal design, that is, the optimal predictor distribution, for the normative sample, thereby maximizing precision of estimation. This is done under five regression models with a quantitative and a categorical predictor, differing in whether they allow for interaction and nonlinearity. Efficient robust designs are given in case of uncertainty about the regression model. Furthermore, formulas are provided to compute the normative sample size such that individuals' positions relative to the derived norms can be assessed with prespecified power and precision. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

This paper studies second-order properties of the many instruments robust t -ratios based on the limited information maximum likelihood and Fuller estimators for instrumental variable regression models with homoskedastic errors under the many instruments asymptotics, where the number of instruments may increase proportionally with the sample size n , and proposes second-order refinements to the t -ratios to improve the size and power properties. Based on asymptotic expansions of the null and non-null distributions of the t -ratios derived under the many instruments asymptotics, we show that the second-order terms of those expansions may have non-trivial impacts on the size as well as the power properties. Furthermore, we propose adjusted t -ratios whose approximation errors for the null rejection probabilities are of order O ( n − 1 ) in contrast to the ones for the unadjusted t -ratios of order O ( n − 1 / 2 ) , and show that these adjustments induce some desirable power properties in terms of the local maximinity. Although these results are derived under homoskedastic errors, we also establish a stochastic expansion for a heteroskedasticity robust t -ratio, and propose an analogous adjustment under slight deviations from homoskedasticity.

Newton-step approximations to pseudo maximum likelihood estimates of spatial autoregressive models with a large number of parameters are examined, in the sense that the parameter space grows slowly as a function of sample size. These have the same asymptotic efficiency properties as maximum likelihood under Gaussianity but are of closed form. Hence they are computationally simple and free from compactness assumptions, thereby avoiding two notorious pitfalls of implicitly defined estimates of large spatial autoregressions. For an initial least squares estimate, the Newton step can also lead to weaker regularity conditions for a central limit theorem than those extant in the literature. A simulation study demonstrates excellent finite sample gains from Newton iterations, especially in large multiparameter models for which grid search is costly. A small empirical illustration shows improvements in estimation precision with real data., 36 pages

This paper studies the optimality of matched-pair designs in randomized controlled trials (RCTs). Matched-pair designs are examples of stratified randomization, in which the researcher partitions a set of units into strata based on their observed covariates and assign a fraction of units in each stratum to treatment. A matched-pair design is such a procedure with two units per stratum. Despite the prevalence of stratified randomization in RCTs, implementations differ vastly. We provide an econometric framework in which, among all stratified randomization procedures, the optimal one in terms of the mean-squared error of the difference-in-means estimator is a matched-pair design that orders units according to a scalar function of their covariates and matches adjacent units. Our framework captures a leading motivation for stratifying in the sense that it shows that the proposed matched-pair design additionally minimizes the magnitude of the ex-post bias, i.e., the bias of the estimator conditional on realized treatment status. We then consider empirical counterparts to the optimal stratification using data from pilot experiments and provide two different procedures depending on whether the sample size of the pilot is large or small. For each procedure, we develop methods for testing the null hypothesis that the average treatment effect equals a prespecified value. Each test we provide is asymptotically exact in the sense that the limiting rejection probability under the null equals the nominal level. We run an experiment on the Amazon Mechanical Turk using one of the proposed procedures, replicating one of the treatment arms in Dellavigna and Pope (2018), and find the standard error decreases by 29%, so that only half of the sample size is required to attain the same standard error.

This paper develops generalized method of moments (GMM) estimation and inference procedures for quantile regression models. We propose a GMM estimator for simultaneous estimation across multiple quantiles. This estimator allows us to model quantile regression coefficients using flexible parametric restrictions across quantiles. The restrictions and simultaneous estimation lead to efficiency gains compared to standard methods. We establish the asymptotic properties of the GMM estimators when the number of quantiles used is fixed and when it diverges to infinity jointly with the sample size. As an alternative to GMM, we also propose a minimum distance estimator over a given subset of quantiles. Moreover, we provide specification tests for the imposed restrictions. The estimators and tests we propose are simple to implement in practice. Monte Carlo simulations provide numerical evidence of the finite sample properties of the methods. Finally, we apply the proposed methods to estimate the effects of smoking on birthweight of live infants at the extreme bottom of the conditional distribution.

Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this paper we explore this issue by first considering the frequentist properties (bias and variance) of the posterior mean in the important case of the normal location model, which consists of a single observation on a univariate Gaussian distribution with unknown mean and known variance. Based on these results, we derive new estimators of the frequentist bias and variance of the WALS estimator in finite samples. We then study the finite-sample performance of the proposed estimators by a Monte Carlo experiment with design derived from a real data application about the effect of abortion on crime rates.

A number of powerful demographic inference methods have been developed in recent years, with the goal of fitting rich evolutionary models to genetic data obtained from many populations. In this paper we investigate the statistical performance of these methods in the specific case where there is continuous migration between populations. Compared with earlier work, migration significantly complicates the theoretical analysis and requires new techniques. We employ the theories of phase-type distributions and concentration of measure in order to study the two-island and isolation-with-migration models, resulting in both upper and lower bounds on rates of convergence for parametric estimators in migration models. For the upper bounds, we consider inferring rates of coalescent and migration on the basis of directly observing pairwise coalescent times, and, more realistically, when (conditionally) Poisson-distributed mutations dropped on latent trees are observed. We complement these upper bounds with information-theoretic lower bounds which establish a limit, in terms of sample size, below which inference is effectively impossible.

We study the finite sample behavior of Lasso-based inference methods such as post double Lasso and debiased Lasso. We show that these methods can exhibit substantial omitted variable biases (OVBs) due to Lasso not selecting relevant controls. This phenomenon can occur even when the coefficients are sparse and the sample size is large and larger than the number of controls. Therefore, relying on the existing asymptotic inference theory can be problematic in empirical applications. We compare the Lasso-based inference methods to modern high-dimensional OLS-based methods and provide practical guidance., Comment: Final author version, accepted at The Review of Economics and Statistics

High-dimensional linear regression has been intensively studied in the community of statistics in the last two decades. For the convenience of theoretical analyses, classical methods usually assume independent observations and sub-Gaussian-tailed errors. However, neither of them hold in many real high-dimensional time-series data. Recently [Sun, Zhou, Fan, 2019, J. Amer. Stat. Assoc., in press] proposed Adaptive Huber Regression (AHR) to address the issue of heavy-tailed errors. They discover that the robustification parameter of the Huber loss should adapt to the sample size, the dimensionality, and the moments of the heavy-tailed errors. We progress in a vertical direction and justify AHR on dependent observations. Specifically, we consider an important dependence structure -- Markov dependence. Our results show that the Markov dependence impacts on the adaption of the robustification parameter and the estimation of regression coefficients in the way that the sample size should be discounted by a factor depending on the spectral gap of the underlying Markov chain.

Conditional value at risk (CVaR) is a popular measure for quantifying portfolio risk. Sensitivity analysis of CVaR is common in risk management and gradient-based optimization algorithms. In this paper, we study the infinitesimal perturbation analysis estimator for CVaR sensitivity using randomized quasi-Monte Carlo (RQMC) simulation. RQMC has proved valuable in financial option pricing with a better rate of convergence compared to Monte Carlo sampling, but theoretical guarantees for this new application of RQMC shall be studied. To this end, we first prove that the RQMC-based estimator is strongly consistent under very mild conditions. Under some technical conditions, RQMC yields a mean error rate of O ( n − 1 / 2 − 1 / ( 4 d − 2 ) + ϵ ) for arbitrarily small ϵ > 0 , where d represents the dimension of RQMC points and n is the sample size. Some typical applications of CVaR sensitivity estimation are conducted to both show how the theoretical results can be applied, as well as to provide numerical results documenting the superiority of the RQMC estimator.

The key statistical properties of the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) estimators were derived in this study for zero mean symmetric error distributions. A density function, named the Approximate Root Normal Distribution (ARND), was developed to approximate the distribution of a square root of a normal random variable. This enabled approximating the distribution of the RMSE estimator. The theoretical derivations and the demonstrations on common distributions, a benchmark time series, and a real world data set (with prediction errors generated from ANN and ARIMA models) lead to the following practically useful findings. When comparing errors having the same distribution type, RMSE was shown to be preferred for platykurtic distributions, MAE for leptokurtic distributions, and either RMSE or MAE for mesokurtic distributions. For different distribution types, however, using the two estimators alone was shown to lead to erroneous conclusions. The revelation that the estimated RMSE/MSE ratio could identify whether the errors came from platykurtic/mesokurtic/leptokurtic distributions was a useful complementary result. Comparison of errors based on, error distributions, sample size and the standard errors of the estimators, was discussed. The proposed procedure for deriving the statistical properties of the two estimators has scope for extension for other distribution types.

Tradeoffs occur when deciding between improving forest inventory precision by increasing sample size or by augmenting cluster plot design factors like size or subplot separation distance. The nature of these tradeoffs changes with variation in type and scale of the spatial pattern of the attribute of interest. To understand the impacts of relationships between type and scale of spatial heterogeneity and cluster plot design efficiency, we constructed a factorial simulation experiment and analysed relationships among forest inventory cost, cluster plot design factors, and different spatial heterogeneity scenarios constructed via simulation. To calculate cost, we constructed a cost model that accounted for both on- and between-plot costs. We found that type and scale of heterogeneity have important implications for plot design choices. Homogeneous stands and landscapes are the least costly to inventory. Subplot area and count have stronger impacts than subplot separation on cost efficiency, particularly in landscapes with aggregated forest patterns and in stands with homogeneous tree patterns. We discuss results in the context of the physical interaction between cluster plot geometry and spatial patterns at different scales, provide computer code for simulations, and suggest principles that forest inventory cluster plot design specialists should consider when designing inventories.

Psychological research often builds on between-group comparisons of (measurements of) latent variables; for instance, to evaluate cross-cultural differences in neuroticism or mindfulness. A critical assumption in such comparative research is that the same latent variable(s) are measured in exactly the same way across all groups (i.e., measurement invariance). Otherwise, one would be comparing apples and oranges. Nowadays, measurement invariance is often tested across a large number of groups by means of multigroup factor analysis. When the assumption is untenable, one may compare group-specific measurement models to pinpoint sources of noninvariance, but the number of pairwise comparisons exponentially increases with the number of groups. This makes it hard to unravel invariances from noninvariances and for which groups they apply, and it elevates the chances of falsely detecting noninvariance. An intuitive solution is clustering the groups into a few clusters based on the measurement model parameters. Therefore, we present mixture multigroup factor analysis (MMG-FA) which clusters the groups according to a specific level of measurement invariance. Specifically, in this article, clusters of groups with metric invariance (i.e., equal factor loadings) are obtained by making the loadings cluster-specific, whereas other parameters (i.e., intercepts, factor (co)variances, residual variances) are still allowed to differ between groups within a cluster. MMG-FA was found to perform well in an extensive simulation study, but a larger sample size within groups is required for recovering more subtle loading differences. Its empirical value is illustrated for data on the social value of emotions and data on emotional acculturation. (PsycInfo Database Record (c) 2022 APA, all rights reserved). ispartof: Psychological Methods vol:27 issue:3 pages:281-306 ispartof: location:United States status: published

The present article aims to investigate the cause-and-effect relationship between the employees’ psychological empowerment (PE) and dimensions of knowledge management (KM) in an oil company, using the fuzzy decision-making trial and evaluation laboratory method. The study population consists of oil company experts. The sample size is determined based on the theoretical saturation limit. The present findings show that PE is the strongest causative factor with significant effects on knowledge creation (KC) and knowledge dissemination (KD). Among the KM dimensions, the most influential factors are the dimensions of KC, knowledge application, and knowledge capture (KCA). Of all KM dimensions, knowledge refinement is the most influential. The KC, in addition to being the most important dimension of KM affected by PE, is also found to influence all other dimensions of KM; this indicates its key role as a starting point in the process of KM. Considering the reciprocal effects of PE and the two dimensions of KM (KC and KD), it is important to pay attention to KC when developing a KM system. Importantly, the present findings show that PE and KM have an interdependent interaction. In other words, not only by improving the employees’ PE, the organizations can accelerate the KM process, but also by improving the KM systems, they may increase their employees’ PE. Based on the sensitivity analyses, our proposed method is as efficient as the available methods, such as interpretive structural modeling and Bayesian best-worst method.

We propose a method for monitoring proportions when the in-control proportion and the sample sizes vary over time. Our approach is able to overcome some of the performance issues of other commonly used methods, as we demonstrate in this paper using analytical and numerical methods. The derivations and results are shown mainly for monitoring proportions, but we show how the method can be extended to the monitoring of count data. Published version

When designing a clinical trial, one key aspect of the design is the sample size calculation. The sample size calculation tends to rely on a target or expected difference. The expected difference can be based on the observed data from previous studies, which results in bias. It has been reported that large treatment effects observed in trials are often not replicated in subsequent trials. If these values are used to design subsequent studies, the sample sizes may be biased which results in an unethical study. Regression to the mean (RTM) is one explanation for this. If only health technologies which meet a particular continuation criterion (such as p

A coalescent model of a sample of size n is derived from a birth–death process that originates at a random time in the past from a single founder individual. Over time, the descendants of the founder evolve into a population of large (infinite) size from which a sample of size n is taken. The parameters and time of the birth–death process are scaled in N 0 , the size of the present-day population, while letting N 0 → ∞ , similarly to how the standard Kingman coalescent process arises from the Wright-Fisher model. The model is named the Limit Birth-Death (LBD) coalescent model. Simulations from the LBD coalescent model with sample size n are computationally slow compared to standard coalescent models. Therefore, we suggest different approximations to the LBD coalescent model assuming the population size is a deterministic function of time rather than a stochastic process. Furthermore, we introduce a hybrid LBD coalescent model, that combines the exactness of the LBD coalescent model model with the speed of the approximations.

Phase II clinical trials in oncology are used to initially evaluate the therapeutic efficacy of a new treatment. In the past, the total response was a frequently used endpoint to access the effectiveness of the treatment. When the total response is modest, clinicians may also be interested in disease control (defined as the total response or stable disease) since it may better predict clinical outcomes. Thus, formally testing both the total response and disease control in a phase II trial has an important clinical implication. In this paper, we propose a new method to construct optimal subset designs for one-stage and two-stage phase II clinical trials with two binary endpoints, i.e. the total response and disease control. A new set of hypotheses under the framework of intersection-union tests is provided in which the treatment is considered promising if both the total response and disease control are good. We show that the power function for each test in a large family of tests is nondecreasing in both the total response rate and disease control rate; identify the parameter configurations at which the maximum Type I error rate and minimum power are achieved and derive level- α tests. We also provide optimal one-stage designs with the minimum sample size and optimal two-stage designs with the least expected total sample size.

This study proposes a new acceptance sampling scheme, namely mean ranked sampling scheme, for efficient decision of statistical quality control. The proposed scheme is based on ranked set sampling under exponential distribution for acceptance or rejection of a lot. Two-point method on operating characteristic function is used for the derivation of plan parameters assuming approximation of exponential to normal distribution. The minimum sample sizes and acceptance numbers are obtained satisfying producer’s and consumer’s risk at certain levels of acceptable (AQL) and tolerable quality (RQL). The main advantages of proposed scheme are (i) data is selected by using free cost sampling method from a large lot and (ii) all units of selected lot are used in making decision. The probability & distribution functions for proposed mean ranked set sampling plan are derived. The OC values comparison with simple random sampling is presented. It is shown that the tables presented here can be used if mean life of units are chosen as a criterion.

The cure fraction models are intended to analyze lifetime data from populations where some individuals are immune to the event under study, and allow a joint estimation of the distribution related to the cured and susceptible subjects, as opposed to the usual approach ignoring the cure rate. In situations involving small sample sizes with many censored times, the detection of nonfinite coefficients may arise via maximum likelihood. This phenomenon is commonly known as monotone likelihood (ML), occurring in the Cox and logistic regression models when many categorical and unbalanced covariates are present. An existing solution to prevent the issue is based on the Firth correction, originally developed to reduce the estimation bias. The method ensures finite estimates by penalizing the likelihood function. In the context of mixture cure models, the ML issue is rarely discussed in the literature; therefore, this topic can be seen as the first contribution of our paper. The second major contribution, not well addressed elsewhere, is the study of the ML issue in cure mixture modeling under the flexibility of a semiparametric framework to handle the baseline hazard. We derive the modified score function based on the Firth approach and explore finite sample size properties of the estimators via a Monte Carlo scheme. The simulation results indicate that the performance of coefficients related to the binary covariates are strongly affected to the imbalance degree. A real illustration, in the melanoma dataset, is discussed using a relatively novel data set collected in a Brazilian university hospital.

The goal of this research is to compare multiple linear regression coefficient estimations with multicollinearity. In order to quantify the effectiveness of estimations by the mean of average mean square error, the ordinary least squares technique (OLS), modified ridge regression method (MRR), and generalized Liu-Kejian method (LKM) are compared (AMSE). For this study, the simulation scenarios are 3 and 5 independent variables with zero mean normally distributed random error of variance 1, 5, and 10, three correlation coefficient levels; i.e., low (0.2), medium (0.5), and high (0.8) are determined for independent variables, and all combinations are performed with sample sizes 15, 55, and 95 by Monte Carlo simulation technique for 1,000 times in total. As the sample size rose, the AMSE decreased. The MRR and LKM both outperformed the LSM. At random error of variance 10, the MRR is the most suitable for all circumstances.

We consider partially observed binary matched-pair data. We assume that the incomplete subjects are missing at random. Within this missing framework, we propose an EM-algorithm based approach to construct an interval estimator of the proportion difference incorporating all the subjects. In conjunction with our proposed method, we also present two improvements to the interval estimator through some correction factors. The performances of the three competing methods are then evaluated through extensive simulation. Recommendation for the method is given based on the ability to preserve type-I error for various sample sizes. Finally, the methods are illustrated in two real-world data sets. An R-function is developed to implement the three proposed methods.

A new lifetime distribution called alpha power modified Weibull (APMW) distribution based on the alpha power transformation method has been studied. Various statistical properties of the newly developed distribution including quantiles, moments, stress-strength parameter, Bonferroni and Lorentz curve, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics have been obtained. Percentage points of the APMW distribution for different values of the parameters have been obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters. A simulation study has been performed to evaluate the behaviour of the MLEs in terms of the sample size n and revealed that as the value of the sample size increases the value of the mean square error decreases showing the reliability of the estimators. The efficiency and flexibility of the new distribution are illustrated by analysing three real-life data sets. In each case, the APMW distribution provides a better fit indicating that the APMW distribution is a justifiable choice for fitting the considered data sets.

In this paper an easy to implement method of stochastically weighing short and long-memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly more accurate than their classic counterparts for each fixed sample size n. It is illustrated both theoretically and numerically that the randomization framework of this paper produces randomized (asymptotic) pivotal quantities, for the mean, which admit central limit theorems with smaller magnitudes of error as compared to those of their leading classic counterparts. An Edgeworth expansion result for randomly weighted linear processes whose innovations do not necessarily satisfy the Cramer condition, is established. Numerical illustrations and applications to real world data are also included.

Summary We consider the problem of testing for the presence of linear relationships between large sets of random variables based on a postselection inference approach to canonical correlation analysis. The challenge is to adjust for the selection of subsets of variables having linear combinations with maximal sample correlation. To this end, we construct a stabilized one-step estimator of the Euclidean norm of the canonical correlations maximized over subsets of variables of prespecified cardinality. This estimator is shown to be consistent for its target parameter and asymptotically normal, provided the dimensions of the variables do not grow too quickly with sample size. We also develop a greedy search algorithm to accurately compute the estimator, leading to a computationally tractable omnibus test for the global null hypothesis that there are no linear relationships between any subsets of variables having the prespecified cardinality. We further develop a confidence interval that takes the variable selection into account.

Small area estimation (SAE) methods can provide information that conventional direct survey estimation methods cannot. The use of small area estimates based on linear and generalized linear mixed models is still very limited, possibly because of the perceived complexity of estimating the root mean square errors (RMSEs) of the estimates. This paper outlines a study used to determine the conditions under which the estimated RMSEs, produced as part of statistical output (‘plug-in’ estimates of RMSEs) could be considered appropriate for a practical application of SAE methods where one of the main requirements was to use SAS software. We first show that the estimated RMSEs created using an EBLUP model in SAS and those obtained using a parametric bootstrap are similar to the published estimated RMSEs for the corn data in the seminal paper by Battese, Harter and Fuller. We then compare plug-in estimates of RMSEs from SAS procedures used to create EBLUP and EBP estimators against estimates of RMSEs obtained from a parametric bootstrap. For this comparison we created estimates of current smoking in males for 153 local government areas (LGAs) using data from the NSW Population Health Survey in Australia. Demographic variables from the survey data were included as covariates, with LGA-level population proportions, obtained mainly from the Australian Census used for prediction. For the EBLUP, the estimated plug-in estimates of RMSEs can be used, provided the sample size for the small area is more than seven. For the EBP, the plug-in estimates of RMSEs are suitable for all in-sample areas, out-of-sample areas need to use estimated RMSEs that use the parametric bootstrap.

The stepped wedge cluster randomized trial (SW-CRT) is an increasingly popular design for evaluating health service delivery or policy interventions. An essential consideration of this design is the need to account for both within-period and between-period correlations in sample size calculations. Especially when embedded in health care delivery systems, many SW-CRTs may have subclusters nested in clusters, within which outcomes are collected longitudinally. However, existing sample size methods that account for between-period correlations have not allowed for multiple levels of clustering. We present computationally efficient sample size procedures that properly differentiate within-period and between-period intracluster correlation coefficients in SW-CRTs in the presence of subclusters. We introduce an extended block exchangeable correlation matrix to characterize the complex dependencies of outcomes within clusters. For Gaussian outcomes, we derive a closed-form sample size expression that depends on the correlation structure only through two eigenvalues of the extended block exchangeable correlation structure. For non-Gaussian outcomes, we present a generic sample size algorithm based on linearization and elucidate simplifications under canonical link functions. For example, we show that the approximate sample size formula under a logistic linear mixed model depends on three eigenvalues of the extended block exchangeable correlation matrix. We provide an extension to accommodate unequal cluster sizes and validate the proposed methods via simulations. Finally, we illustrate our methods in two real SW-CRTs with subclusters.

A random delayed treatment effect is expected in a confirmatory clinical trial for an immunotherapy due to the individual heterogeneity of physiological conditions. For this reason, the delay time will be assumed to follow a continuous distribution that is difficult to estimate accurately based on the early-phase data, which hinders the specification of the most powerful weighted log-rank test. Therefore, we propose a simulation-based maximum duration design with a robustly powerful Maxcombo test for a group sequential trial for the immunotherapy with the random delayed treatment effect. The design obtains the group sequential boundaries by a simulation procedure and determines the required maximum sample size using a one-dimensional search in which another simulation procedure is used to calculate empirical power. The simulation researches proved the accuracy of the group sequential boundaries and their robustness against the misspecified maximum sample sizes for large samples and revealed their moderate sensitivity against the misspecified survival distributions under the null hypothesis of no difference. The studies investigated whether the type I error rate would inflate under the "inferior" null hypothesis and evaluated the robustness against different distributions of the delay time in terms of the empirical power among the Maxcombo tests and component weighted log-rank tests.

A recently proposed SLOPE estimator (arXiv:1407.3824) has been shown to adaptively achieve the minimax $\ell_2$ estimation rate under high-dimensional sparse linear regression models (arXiv:1503.08393). Such minimax optimality holds in the regime where the sparsity level $k$, sample size $n$, and dimension $p$ satisfy $k/p \rightarrow 0$, $k\log p/n \rightarrow 0$. In this paper, we characterize the estimation error of SLOPE under the complementary regime where both $k$ and $n$ scale linearly with $p$, and provide new insights into the performance of SLOPE estimators. We first derive a concentration inequality for the finite sample mean square error (MSE) of SLOPE. The quantity that MSE concentrates around takes a complicated and implicit form. With delicate analysis of the quantity, we prove that among all SLOPE estimators, LASSO is optimal for estimating $k$-sparse parameter vectors that do not have tied non-zero components in the low noise scenario. On the other hand, in the large noise scenario, the family of SLOPE estimators are sub-optimal compared with bridge regression such as the Ridge estimator., 50 pages, 18 figures

El presente estudio tuvo como objetivo evaluar la eficiencia estadística de seis estimadores de muestreo para plantear una estrategia de muestreo óptima en términos de precisión y tiempo que permita realizar inventarios maderables operativos que apoyen la toma de decisiones orientadas a mejorar el manejo técnico de plantaciones forestales comerciales de Tectona grandis (teca), establecidas en Campeche, México. Para ello, se evaluaron 8 830 sitios de muestreo ubicados en 2 207.5 hectáreas. Cada sitio rectangular de 72 m2 incluyó nueve cepas, se contabilizó el número de árboles vivos y se midió el diámetro normal. La altura total y volumen por árbol se estimaron con modelos tipo Chapman-Richards y Schumacher-Hall, respectivamente. El área basal y el volumen total por sitio se proyectó a nivel de hectárea. Se estratificó por clase de edad; el área basal y la edad de la plantación se utilizaron como variables auxiliares. La estrategia de muestreo para estimar el volumen medio se conformó al asociar como diseño de muestreo al muestreo simple al azar con el estimador de razón específica en muestreo estratificado, con una estratificación por clases de edad de un año y el área basal como variable auxiliar, esto dio la precisión de 0.21 %. El tamaño de muestra en el muestreo estratificado se redujo 68.3 %, con precisión de 2.5 % del muestreo original, lo cual implica que el esfuerzo de muestreo y el tiempo de ejecución para realizar el inventario operativo puede reducirse, con la consecuente disminución de los costos implícitos.

Modeling the relationship between some climatic determinants in the wet or cropping season of Makurdi, Benue State, Nigeria requires data aggregation. The consequence of this aggregation is the reduction in data sample size. This poses serious challenge of lack of model-fit when the Classical Linear Regression Modeling Approach is employed. The Bayesian Normal Regression Modeling Approach was therefore employed in surmounting this problem. Three Bayesian Normal Regression Models were fitted namely; the Solar radiation, Total Rainfall Amount and the Number of Dry Days model. Each model result was compared with that of its Classical model counterpart. The discrepancies observed were blamed on the sample size reduction. The results of the Bayesian models revealed that; Solar radiation increases by 0.791 MJ/m2 for each unit increase in the natural logarithm of Relative humidity. While it increases by 0.895 MJ/m2 for each unit increase in the natural logarithm of Wind speed. Total Rainfall Amount increases by 66.280 mm for each unit increase in the natural logarithm of the Number of Dry Days while it increases by 2.912 mm for each unit increase in the natural logarithm of the Number of Wet Days. Furthermore, the Number of Dry Days decreases by 6.905 days for each unit increase in the natural logarithm of Number of Wet days, while it increases by 2.028 days for each unit increase in the natural logarithm of Total Rainfall Amount. The study affirmed that the cropping season climate of Makurdi is becoming

We provide asymptotic theory for certain functions of the sample autocovariance matrices of a high-dimensional time series with infinite fourth moment. The time series exhibits linear dependence across the coordinates and through time. Assuming that the dimension increases with the sample size, we provide theory for the eigenvectors of the sample autocovariance matrices and find explicit approximations of a simple structure, whose finite sample quality is illustrated for simulated data. We also obtain the limits of the normalized eigenvalues of functions of the sample autocovariance matrices in terms of cluster Poisson point processes. In turn, we derive the distributional limits of the largest eigenvalues and functionals acting on them. In our proofs, we use large deviation techniques for heavy-tailed processes, point process techniques motivated by extreme value theory, and related continuous mapping arguments., 28 pages

Linear discriminant analysis (LDA) is perhaps one of the most fundamental statistical pattern recognition techniques. In this work, we explicitly present, for the first time, an asymptotically exact estimator of the LDA optimal intercept in terms of achieving the lowest overall risk in the classification of two multivariate Gaussian distributions with a common covariance matrix and arbitrary misclassification costs. The proposed estimator of the optimal bias term is developed based on the theory of random matrices of increasing dimension in which the observation dimension and the sample size tend to infinity while keeping their magnitudes comparable. The simple form of this estimator provides us with some analytical insights into the working mechanism of the bias correction in LDA. We then complement these analytical insights with numerical experiments. In particular, empirical results using real data show that insofar as the overall risk is concerned, the proposed bias-corrected form of LDA can outperform the conventional LDA classifier in a wide range of misclassification costs. At the same time, the superiority of the proposed form over LDA tends to be more evident as dimensionality or the ratio between class-specific costs increase.

In planning randomized clinical trials (RCTs) for diseases such as Alzheimer's disease (AD), researchers frequently rely on the use of existing data obtained from only two time points to estimate sample size via the subtraction of baseline from follow-up measurements in each subject. However, the inadequacy of this method has not been reported. The aim of this study is to discuss the limitation of sample size estimation based on the subtraction of available data from only two time points for RCTs. Mathematical equations are derived to demonstrate the condition under which the obtained data pairs with variable time intervals could be used to adequately estimate sample size. The MRI-based hippocampal volume measurements from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and Monte Carlo simulations (MCS) were used to illustrate the existing bias and variability of estimates. MCS results support the theoretically derived condition under which the subtraction approach may work. MCS also show the systematically under- or over-estimated sample sizes by up to 32.27 % bias. Not used properly, such subtraction approach outputs the same sample size regardless of trial durations partly due to the way measurement errors are handled. Estimating sample size by subtracting two measurements should be treated with caution. Such estimates can be biased, the magnitude of which depends on the planned RCT duration. To estimate sample sizes, we recommend using more than two measurements and more comprehensive approaches such as linear mixed effect models.

Each cluster consists of multiple subunits from which outcome data are collected. In a subunit randomization trial, subunits are randomized into different intervention arms. Observations from subunits within each cluster tend to be positively correlated due to the shared common frailties, so that the outcome data from a subunit randomization trial have dependency between arms as well as within each arm. For subunit randomization trials with a survival endpoint, few methods have been proposed for sample size calculation showing the clear relationship between the joint survival distribution between subunits and the sample size, especially when the number of subunits from each cluster is variable. In this paper, we propose a closed form sample size formula for weighted rank test to compare the marginal survival distributions between intervention arms under subunit randomization, possibly with variable number of subunits among clusters. We conduct extensive simulations to evaluate the performance of our formula under various design settings, and demonstrate our sample size calculation method with some real clinical trials.

A centered $$L^2$$ -norm based test statistic is used for testing if a high-dimensional mean vector equals zero where the data dimension may be much larger than the sample size. Inspired by the fact that under some regularity conditions the asymptotic null distributions of the proposed test are the same as the limiting distributions of a chi-square-mixture, a three-cumulant matched chi-square-approximation is suggested to approximate this null distribution. The asymptotic power of the proposed test under a local alternative is established and the effect of data non-normality is discussed. A simulation study under various settings demonstrates that in terms of size control, the proposed test performs significantly better than some existing competitors. Several real data examples are presented to illustrate the wide applicability of the proposed test to a variety of high-dimensional data analysis problems, including the one-sample problem, paired two-sample problem, and MANOVA for correlated samples or independent samples.

Background The size of the margin strongly influences the required sample size in non-inferiority and equivalence trials. What is sometimes ignored, however, is that for trials with binary outcomes, the scale of the margin – risk difference, risk ratio or odds ratio – also has a large impact on power and thus on sample size requirement. When considering several scales at the design stage of a trial, these sample size consequences should be taken into account. Sometimes, changing the scale may be needed at a later stage of a trial, for example, when the event proportion in the control arm turns out different from expected. Also after completion of a trial, a switch to another scale is sometimes made, for example, when using a regression model in a secondary analysis or when combining study results in a meta-analysis that requires unifying scales. The exact consequences of such switches are currently unknown. Methods and Results This article first outlines sample size consequences for different choices of analysis scale at the design stage of a trial. We add a new result on sample size requirement comparing the risk difference scale with the risk ratio scale. Then, we study two different approaches to changing the analysis scale after the trial has commenced: (1) mapping the original non-inferiority margin using the event proportion in the control arm that was anticipated at the design stage or (2) mapping the original non-inferiority margin using the observed event proportion in the control arm. We use simulations to illustrate consequences on type I and type II error rates. Methods are illustrated on the INES trial, a non-inferiority trial that compared single birth rates in subfertile couples after different fertility treatments. Our results demonstrate large differences in required sample size when choosing between risk difference, risk ratio and odds ratio scales at the design stage of non-inferiority trials. In some cases, the sample size requirement is twice as large on one scale compared with another. Changing the scale after commencing the trial using anticipated proportions mainly impacts type II error rate, whereas switching using observed proportions is not advised due to not maintaining type I error rate. Differences were more pronounced with larger margins. Conclusions Trialists should be aware that the analysis scale can have large impact on type I and type II error rates in non-inferiority trials.

We consider the General Linear Model (GLM) which includes multivariate analysis of variance (MANOVA) and multiple linear regression as special cases. In practice, there are several widely used criteria for GLM: Wilks’ lambda, Bartlett–Nanda–Pillai test, Lawley–Hotelling test, and Roy maximum root test. Limiting distributions for the first three mentioned tests are known under different asymptotic settings. In the present paper, we obtain computable error bounds for the normal approximation of the Lawley–Hotelling statistic when the dimension grows proportionally to the sample size. This result enables us to get more precise calculations of the p-values in applications of multivariate analysis. In practice, more and more often analysts encounter situations where the number of factors is large and comparable with the sample size. Examples include medicine, biology (i.e., DNA microarray studies), and finance.

Spatial effects are often simultaneously investigated with non-linear effects of continuous covariates and the usual linear effect. In this work the performance of models with and without spatial dependence in partitioned (PM) and non-partitioned models (NPM) for four (4) censoring percentages, three(3) levels of Weibull baseline variances (WBV), and sample sizes 100, 500 & 1000 were investigated. Hazard models were adapted to the generalized additive predictors and analyses were carried out via MCMC simulation technique. The performances of the models were again assessed when fitted to the diabetic data set. Results suggest that; partition models outperformed the non-partition ones. Models with spatial dependence perform better than models without spatial dependence in denser event times and when WBVs are low. The partition models perform better with spatial dependence than the Non-partitioned models. For the diabetic data set, it is seen that covariates Age and Blood Sugar level (BSL) violates the proportionality assumptions upon test. Further assessment from the graph of coefficient against time; suggest that Age be put to cut-points while BSL was estimated for models with and without Penalized splines for the sake of comparison, since the graph shows just a slight deviation from proportionality. Hazard rates for the time varying Age; indicate that as the time of study rolls by, the hazard of experiencing the event death from the disease increases steadily between intervals but constant within each time interval. A unit change in hazard rate for BSL indicates a decrease for PM implemented for with and without penalized splines. The model without penalized splines was however, seen to be better with smaller DIC (Deviance Information Criteria) value. Marriage is seen to be significant in the management of the disease in comparison to single patients. In addition patients are advised to visit their physicians on a regular basis to run a routine check to keep their BSL in good range. The study provides a means of moving out of non-linear ruts in survival data analysis. Intervals increase sample sizes (pseudoobservations), which in turn improves the modified Partitioned model when they are with or without spatial dependence.

Author(s): Zheng, Bang Quan | Advisor(s): Bentler, Peter M | Abstract: Does Reweighted Least Squares (RLS) perform better in small samples than maximum likelihood (ML) for mean and covariance structure? ML statistics in covariance structure analysis are based on the asymptotic normality assumption; however, actual applications of structural equation modeling (SEM) in social and behavioral science research usually involve small samples. It has been found that chi-square tests often incorrectly over-reject the null hypothesis: Σ=Σ(θ), because when sample is small the sample covariance matrix becomes ill-conditioned and entails unstable estimates. In certain SEM models, the vector of parameter must contain both means, variances and covariances. Yet, whether RLS also works in mean and covariance structure remains unexamined. This research is an extended examination of reweighted least squares in mean and covariance structure. Specifically, we replace biased covariance matrix in traditional GLS function (Browne, 1974) with the unbiased sample covariance matrix that derives from ML estimation. Moreover, under the assumption of multivariate normality, a Monte Carlo simulation study was carried out to examine the statistical performance as compared with ML methods in different sample sizes. Based on empirical rejection frequencies and empirical averages of test statistic, this study shows that RLS performs much better than ML in mean and covariance structure models when sample sizes are small.

PurposeAs an alternative to the standard p and np charts along with their various modifications, beta control charts are used in the literature for monitoring proportion data. These charts in general use average of proportions to set up the control limits assuming in-control parameters known. The purpose of the paper is to propose a control chart for detecting shift(s) in the percentiles of a beta distributed process monitoring scheme when in-control parameters are unknown. Such situations arise when specific percentile of proportion of conforming or non-conforming units is the quality parameter of interest.Design/methodology/approachParametric bootstrap method is used to develop the control chart for monitoring percentiles of a beta distributed process when in-control parameters are unknown. Extensive Monte Carlo simulations are conducted for various combinations of percentiles, false-alarm rates and sample sizes to evaluate the in-control performance of the proposed bootstrap control charts in terms of average run lengths (ARL). The out-of-control behavior and performance of the proposed bootstrap percentile chart is thoroughly investigated for several choices of shifts in the parameters of beta distribution. The proposed chart is finally applied to two skewed data sets for illustration.FindingsThe simulated values of in-control ARL are found to be closer to the theoretical results implying that the proposed chart for percentiles performs well with both positively and negatively skewed data. Also, the out-of-control ARL values for the percentiles decrease sharply with both downward and upward small, medium and large shifts in the parameters. The phenomenon indicates that the chart is effective in detecting shifts in the parameters. However, the speed of detection of shifts varies depending on the type of shift, the parameters and the percentile being considered. The proposed chart is found to be effective in comparison to the Shewhart-type chart and bootstrap-based unit gamma chart.Originality/valueIt is worthwhile to mention that the beta control charts proposed in the literature use average of proportion to set up the control limits. However, in practice, specific percentile of proportion of conforming or non-conforming items should be more useful as the quality parameter of interest than average. To the best of our knowledge, no research addresses beta control chart for percentiles of proportion in the literature. Moreover, the proposed control chart assumes in-control parameters to be unknown, and hence captures additional variability introduced into the monitoring scheme through parameter estimation. In this sense, the proposed chart is original and unique.

We consider a random censoring model for survival analysis, allowing the possibility that only a proportion of individuals in the population are susceptible to death or failure, and the remainder are immune or cured. Susceptibles suffer the event under study eventually, but the time at which this occurs may not be observed due to censoring. Immune individuals have infinite lifetimes which are always censored in the sample. Assuming that the distribution of the susceptibles’ lifetimes as well as the censoring distribution have infinite right endpoints and are in the domain of attraction of the Gumbel distribution, we obtain asymptotic distributions, as sample size tends to infinity, of statistics relevant to testing for the possible existence of immunes in the population.

The extrapolation of quantiles beyond or below the largest or smallest observation plays an important role in hydrological practice, design of hydraulic structures, water resources management, or risk assessment. Traditionally, extreme quantiles are obtained using parametric methods that require to make an a priori assumption about the distribution that generated the data. This approach has several limitations mainly when applied to the tails of the distribution. Semiparametric or nonparametric methods, on the other hand, allow more flexibility and they may overcome the problems of the parametric approach. Therefore, we present here a comparison between three selected semi/nonparametric methods, namely the methods of Hutson (Stat and Comput, 12(4):331–338, 2002) and Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) and kernel density estimation. While the first and third methods have already applications in hydrology, Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information and Support Services, Seattle, WA, United States of America, 1995) is proposed in this context for the first time. After describing the methods and their applications in hydrology, we compare their performance for different sample lengths and return periods. We use synthetic samples extracted from four distributions whose maxima belong to the Gumbel, Weibull, and Fréchet domain of attraction. Then, the same methods are applied to a real precipitation dataset and compared with a parametric approach. Eventually, a detailed discussion of the results is presented to guide researchers in the choice of the most suitable method. None of the three methods, in fact, outperforms the others; performances, instead, vary greatly with distribution type, return period, and sample size.

Outlier detection is a challenging task especially when outliers are defined by rare combinations of multiple variables. In this paper, we develop and evaluate a new method for the detection of outliers in multivariate data that relies on Principal Components Analysis (PCA) and three-sigma limits. The proposed approach employs PCA to effectively perform dimension reduction by regenerating variables, i.e., fitted points from the original observations. The observations lying outside the three-sigma limits are identified as the outliers. This proposed method has been successfully employed to two real life and several artificially generated datasets. The performance of the proposed method is compared with some of the existing methods using different performance evaluation criteria including the percentage of correct classification, precision, recall, and F-measure. The supremacy of the proposed method is confirmed by abovementioned criteria and datasets. The F-measure for the first real life dataset is the highest, i.e., 0.6667 for the proposed method and 0.3333 and 0.4000 for the two existing approaches. Similarly, for the second real dataset, this measure is 0.8000 for the proposed approach and 0.5263 and 0.6315 for the two existing approaches. It is also observed by the simulation experiments that the performance of the proposed approach got better with increasing sample size.

The classical two-sample t-test is not robust to skewed populations, and the large sample approximation has low accuracy for finite sample sizes. This paper presents two new types of tests, the TCF...

We emphasize that it is possible to improve the principle of unbiased risk estimation for model selection by addressing excess risk deviations in the design of penalization procedures. Indeed, we propose a modification of Akaike's Information Criterion that avoids overfitting, even when the sample size is small. We call this correction an over-penalization procedure. As proof of concept, we show the nonasymptotic optimality of our histogram selection procedure in density estimation by establishing sharp oracle inequalities for the Kullback-Leibler divergence. One of the main features of our theoretical results is that they include the estimation of unbounded logdensities. To do so, we prove several analytical and probabilistic lemmas that are of independent interest. In an experimental study, we also demonstrate state-of-the-art performance of our over-penalization criterion for bin size selection, in particular outperforming AICc procedure., This is a further version of the preprint entitled "Model Selection as a Multiple Testing Procedure: Improving Akaike's Information Criterion"

Seemingly unrelated mixed-effects models were used to model biomass models for Larix olgensis, Pinus koraiensis, and Pinus sylvestris, and the developed models considered multiple variables to enhance the practicality of the models. Korean larch (Larix olgensis), Korean pine (Pinus koraiensis), and Mongolian pine (Pinus sylvestris) are important coniferous species in the northeastern area of the P.R. China; hence, accurate biomass estimates of these species are meaningful for evaluating forest health and calculating carbon storage. Based on the tree variables of diameter at breast height ( $$DBH$$ ), tree height ( $$H$$ ), age, live crown length and crown width, three log-transformed species-specific biomass functions were developed using linear seemingly unrelated regression (SUR) since the error structures of the component biomass model (stem, branches, foliage and roots) were proven to be multiplicative. Furthermore, the plot-level random effect was introduced into the SUR model, namely the SURM model, to achieve more accurate biomass estimates. The results showed that the SURM model has a better fitting performance than the SUR models for three species and model types. The determination coefficient, $${R}^{2}$$ , was always larger for the SURM models than for the corresponding SUR models, while the root mean square error, $${\text{RMSE}}$$ , was always smaller for the SURM models. By leave-one-out validation, the SURM models were proven to provide more accurate predictions because the mean prediction percent error ( $${\text{MPE}}$$ ) was close to 0 and the mean absolute percentage error ( $${\text{MAPE}}$$ ) was smaller than that of the corresponding SUR models across species and model types. In addition, the size and design of the sample used to calibrate for random effects were assessed using the $${\text{MAPE}}$$ statistical index, $${\text{MAPE}}$$ . The calibration of the SURM showed a decreasing pattern of bias as the sample size increased, indicating that more available sampled trees improved the prediction accuracy of SURM models, while only slight differences existed across sampling designs. Overall, the newly developed biomass models have advantages in various data structures, and will be meaningful and useful in terms of accurately predicting the biomass of three important species in Northeast China.