Search

One fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates. We propose a semiparametric framework for identifying such effect modification. Instead of using the traditional outcome models, we directly posit semiparametric models on contrasts, or expected differences of the outcome under different treatment choices or exposures. Through semiparametric estimation theory, all valid estimating equations, including the efficient scores, are derived. Besides doubly robust loss functions, our approach also enables dimension reduction in presence of many covariates. The asymptotic and non-asymptotic properties of the proposed methods are explored via a unified statistical and algorithmic analysis. Comparison with existing methods in both simulation and real data analysis demonstrates the superiority of our estimators especially for an efficiency improved version. for this article are available online. [ABSTRACT FROM AUTHOR]

The "New Statistics" emphasizes effect sizes, confidence intervals, meta-analysis, and the use of Open Science practices. We present three specific ways in which a New Statistics approach can help improve scientific practice: by reducing overconfidence in small samples, by reducing confirmation bias, and by fostering more cautious judgments of consistency. We illustrate these points through consideration of the literature on oxytocin and human trust, a research area that typifies some of the endemic problems that arise with poor statistical practice. [ABSTRACT FROM AUTHOR]

The authors offer a response to the commentaries made on their article on statistical estimation and privacy. They discuss the issues raised by the discussants including the advantages and disadvantages of local notions of privacy as compared to classical differential and approximate differential privacy, the issue of interactivity, and the importance of local differential privacy. The goal of statistical inference is also mentioned.

The classical birthday problem considers the probability that at least two people in a group of sizeNshare the same birthday. The inverse birthday problem considers the estimation of the sizeNof a group given the number of different birthdays in the group. In practice, this problem is analogous to estimating the size of a population from occurrence data only. The inverse problem can be solved via two simple approaches including the method of moments for a multinominal model and the maximum likelihood estimate of a Poisson model, which we present in this study. We investigate properties of both methods and show that they can yield asymptotically equivalent Wald-type interval estimators. Moreover, we show that these methods estimate a lower bound for the population size when birth rates are nonhomogenous or individuals in the population are aggregated. A simulation study was conducted to evaluate the performance of the point estimates arising from the two approaches and to compare the performance of seven interval estimators, including likelihood ratio and log-transformation methods. We illustrate the utility of these methods by estimating: (1) the abundance of tree species over a 50-hectare forest plot, (2) the number of Chlamydia infections when only the number of different birthdays of the patients is known, and (3) the number of rainy days when the number of rainy weeks is known. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

The article presents comment on the study regarding the parameter and model selection for general smooth models. It explores the development of a framework which is flexible and more likely to shape the routine use of smooth models. It also commends the researchers for their significant contribution to the development of smooth models and estimation.

In the past 20 years, there has been a staggering increase in the use of Bayesian statistical inference, based on Markov chain Monte Carlo (MCMC)methods, to estimate model parameters and other quantities of interest. This trend exists in virtually all areas of engineering and science. In a typical application, researcherswill report estimates of parametric functions (e.g., quantiles, probabilities, or predictions of future outcomes) and corresponding intervals from MCMC methods. One difficulty with the use of inferentialmethods based on Monte Carlo (MC) is that reported results may be inaccurate due to MC error. MC error, however, can be made arbitrarily small by increasing the number of MC draws. Most users of MCMC methods seem to use indirect diagnostics, trial-and-error, or guess-work to decide how long to run a MCMC algorithm and accuracy of MCMC output results is rarely reported. Unless careful analysis is done, reported numerical results may contain digits that are completely meaningless. In this article, we describe an algorithm to provide direct guidance on the number of MCMC draws needed to achieve a desired amount of precision (i.e., a specified number of accurate significant digits) for Bayesian credible interval endpoints. [ABSTRACT FROM AUTHOR]

Bayesian credible interval (CI) estimation is a statistical procedure that has been well addressed in both the theoretical and applied literature. Parametric assumptions regarding baseline data distributions are critical for the implementation of this method. We provide a nonparametric technique for incorporating prior information into the equal-tailed (ET) and highest posterior density (HPD) CI estimators in the Bayesianmanner. We propose to use a data-driven likelihood function, replacing the parametric likelihood function to create a distribution-free posterior. Higher order asymptotic propositions are derived to show the efficiency and consistency of the proposed method. We demonstrate that the proposed approach may correct confidence regions with respect to skewness of the data distribution. An extensive Monte Carlo (MC) study confirms the proposed method significantly outperforms the classical CI estimation in a frequentist context. A real data example related to a study of myocardial infarction illustrates the excellent applicability of the proposed technique. Supplementary material, including the R code used to implement the developed method, is available online. [ABSTRACT FROM AUTHOR]

An important practical problem for statistical agencies and central banks that publish economic data is the seasonal adjustment of mixed frequency stock and flow time series. This may arise in practice due to changes in funding of a particular survey. Mathematically, the problem can be reduced to the need to compute imputations, forecasts, and backcasts from a given model of the highest available frequency data. The nonstationarity of the economic time series coupled with the alteration of sampling frequency makes the problem of model estimation and imputation challenging. For flow data the analysis cannot be recast as a missing value problem, so that time series imputation methods are ineffective. We provide explicit formulas and algorithms that allow one to compute the log Gaussian likelihood of the mixed sample, as well as any imputations and forecasts. Formulas for the relevant mean squared error are also derived. We evaluate the methodology through simulations, and illustrate the techniques on some economic time series. [ABSTRACT FROM PUBLISHER]

In recent years, “reproducibility” has emerged as a key factor in evaluating x applications of statistics to the biomedical sciences, for example, learning predictors of disease phenotypes from high-throughput “omics” data. In particular, “validation” is undermined when error rates on newly acquired data are sharply higher than those originally reported. More precisely, when data are collected fromm“studies” representing possibly different subphenotypes, more generally different mixtures of subphenotypes, the error rates in cross-study validation (CSV) are observed to be larger than those obtained in ordinary randomized cross-validation (RCV), although the “gap” seems to close asmincreases. Whereas these findings are hardly surprising for a heterogenous underlying population, this discrepancy is then seen as a barrier to translational research. We provide a statistical formulation in the large-sample limit: studies themselves are modeled as components of a mixture and all error rates are optimal (Bayes) for a two-class problem. Our results cohere with the trends observed in practice and suggest what is likely to be observed with large samples and consistent density estimators, namely, that the CSV error rate exceeds the RCV error rates for anym, the latter (appropriately averaged) increases withm, and both converge to the optimal rate for the whole population. [ABSTRACT FROM PUBLISHER]

This article presents a counterintuitive result regarding the estimation of a regression slope coefficient. Paradoxically, the precision of the slope estimator can deteriorate when additional information is used to estimate its value. In a randomized experiment, the distribution of baseline variables should be identical across treatments due to randomization. The motivation for this article came from noting that the precision of slope estimators deteriorated when pooling baseline predictors across treatment groups. [ABSTRACT FROM AUTHOR]

We examine the application of a Poisson common factor model for the projection of mortality jointly for females and males. The model structure is an extension of the classical Lee–Carter method in which there is a common factor for the aggregate population, while a number of additional sex-specific factors can also be incorporated. The Poisson distribution is a natural choice for modelling the number of deaths, and its use provides a formal statistical framework for model selection, parameter estimation, and data analysis. Our results for Australian data show that this model leads to projected life expectancy values similar to those produced by the separate projection of mortality for females and males, but possesses the additional advantage of ensuring that the projected male-to-female ratio for death rates at each age converges to a constant. Moreover, the randomness of the corresponding residuals indicates that the model fit is satisfactory. [ABSTRACT FROM AUTHOR]

Information on flood seasonality is required in many practical applications, such as estimation of seasonal design floods, flood forecasting and protection, flood-plain management and operation of water resources systems. Directional statistics (DS) and relative frequency (RF) are two of the popular methods for identifying flood seasonality. A new method, which is an improvement over DS, the IDS method, is proposed to identify flood seasonality and partition the flood season into sub-seasons. The performance of the IDS method was evaluated using synthetic data as well as observed data. The RF, DS and IDS methods were applied to the Geheyan and Baishan reservoir basins in China, and their results were compared and analysed. The results of flood seasonality identified by the IDS method were more objective than those of the RF and DS methods. [ABSTRACT FROM AUTHOR]

In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covariance matrices under the spectral norm. In contrast, the commonly used universal thresholding estimators are shown to be suboptimal over the same parameter spaces. Support recovery is discussed as well. The adaptive thresholding estimators are easy to implement. The numerical performance of the estimators is studied using both simulated and real data. Simulation results demonstrate that the adaptive thresholding estimators uniformly outperform the universal thresholding estimators. The method is also illustrated in an analysis on a dataset from a small round blue-cell tumor microarray experiment. A supplement to this article presenting additional technical proofs is available online. [ABSTRACT FROM AUTHOR]

Statistics are developed to test for the presence of an asymptotic discontinuity (or infinite density or peakedness) in a probability density at the median. The approach makes use of work by Knight (1998) on L1 estimation asymptotics in conjunction with nonparametric kernel density estimation methods. The size and power of the tests are assessed, and conditions under which the tests have good performance are explored in simulations. The new methods are applied to stock returns of leading companies across major U.S. industry groups. The results confirm the presence of infinite density at the median as a new significant empirical evidence for stock return distributions. [ABSTRACT FROM AUTHOR]

This article is about S-estimation for penalized regression splines. Penalized regression splines are one of the currently most used methods for smoothing noisy data. The estimation method used for fitting such a penalized regression spline model is mostly based on least squares methods, which are known to be sensitive to outlying observations. In real-world applications, outliers are quite commonly observed. There are several robust estimation methods taking outlying observations into account. We define and study S-estimators for penalized regression spline models. Hereby we replace the least squares estimation method for penalized regression splines by a suitable S-estimation method. By keeping the modeling by means of splines and by keeping the penalty term, though using S-estimators instead of least squares estimators, we arrive at an estimation method that is both robust and flexible enough to capture nonlinear trends in the data. Simulated data and a real data example are used to illustrate the effectiveness of the procedure. Software code (for use with R) is available online. [ABSTRACT FROM AUTHOR]

The offset-normal shape distribution is defined as the induced shape distribution of a Gaussian distributed random configuration in the plane. Such distributions were introduced by Dryden and Mardia (1991) and represent an important parameterized family of shape distributions for shape analysis. This article reports a method for performing maximum likelihood estimation of parameters involved. The method consists of an EM algorithm with simple update rules and is shown to be easily applicable in many practical examples. We also show the necessary adjustments needed for using this algorithm for shape regression, missing landmark data, and mixtures of offset-normal shape distributions. [ABSTRACT FROM AUTHOR]

The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric estimation of the optimal importance sampling distribution (known as "nonparametric importance sampling") is a reasonable alternative to parametric approaches. In this article, nonparametric variants of both the self-normalized and the unnormalized importance sampling estimator are proposed and investigated. A common critique of nonparametric importance sampling is the increased computational burden compared with parametric methods. We solve this problem to a large degree by utilizing the linear blend frequency polygon estimator instead of a kernel estimator. Mean square error convergence properties are investigated, leading to recommendations for the efficient application of nonparametric importance sampling. Particularly, we show that nonparametric importance sampling asymptotically attains optimal importance sampling variance. The efficiency of nonparametric importance sampling algorithms relies heavily on the computational efficiency of the nonparametric estimator used. The linear blend frequency polygon outperforms kernel estimators in terms of certain criteria such as efficient sampling and evaluation. Furthermore, it is compatible with the inversion method for sample generation. This allows one to combine nonparametric importance sampling with other variance reduction techniques such as stratified sampling. Empirical evidence for the usefulness of the suggested algorithms is obtained by means of three benchmark integration problems. We show empirically that these methods may work in higher dimensions, at least up to dimension eight. As an application, we estimate the distribution of the queue length of a spam filter queuing system based on real data. [ABSTRACT FROM AUTHOR]

Interest in predicting protein backbone conformational angles has prompted the development of modeling and inference procedures for bivariate angular distributions. We present a Bayesian approach to density estimation for bivariate angular data that uses a Dirichlet process mixture model and a bivariate von Mises distribution. We derive the necessary full conditional distributions to fit the model, as well as the details for sampling from the posterior predictive distribution. We show how our density estimation method makes it possible to improve current approaches for protein structure prediction by comparing the performance of the so-called "whole" and "half" position distributions. Current methods in the field are based on whole position distributions, as density estimation for the half positions requires techniques, such as ours, that can provide good estimates for small datasets. With our method we are able to demonstrate that half position data provides a better approximation for the distribution of conformational angles at a given sequence position, therefore providing increased efficiency and accuracy in structure prediction. [ABSTRACT FROM AUTHOR]

Ecologists use the relative abundance of fossil pollen in sediments to estimate how tree species abundances change over space and time. To predict historical forest composition and quantify the available information, we build a Bayesian hierarchical model of forest composition in central New England, USA, based on pollen in a network of ponds. The critical relationships between abundances of taxa in the pollen record and abundances as actual vegetation are estimated for the modern and colonial periods, for which both pollen and direct vegetation data are available, based on a latent multivariate spatial process representing forest composition. For time periods in the past with only pollen data, we use the estimated model parameters to constrain predictions about the latent spatio-temporal process conditional on the pollen data. We develop an innovative graphical assessment of feature significance to help to infer which spatial patterns are reliably estimated. The model allows us to estimate the spatial distribution and relative abundances of tree species over the last 2,500 years, with an assessment of uncertainty, and to draw inference about how these patterns have changed over time. Cross-validation suggests that our feature significance approach can reliably indicate certain large-scale spatial features for many taxa, but that features on scales smaller than 50 km are difficult to distinguish, as are large-scale features for some taxa. We also use the model to quantitatively investigate ecological hypotheses, including covariate effects on taxa abundances and questions about pollen dispersal characteristics. The critical advantages of our modeling approach over current ecological analyses are the explicit spatio-temporal representation, quantification of abundance on the scale of trees rather than pollen, and uncertainty characterization. [ABSTRACT FROM AUTHOR]

A major task in understanding biological processes is to elucidate the relationships between genes involved in the underlying biological pathways. Microarray data from an increasing number of biologically interrelated experiments now allows for more complete portrayals of functional gene relationships in the pathways. In current studies of gene relationships, the presence of expression dependencies attributable to the biologically interrelated experiments, however, has been widely ignored. When unaccounted for, these (experiment) dependencies can result in inaccurate inferences of functional gene relationships, and hence incorrect biological conclusions. This article contributes a framework consisting of a model and an estimation procedure to infer gene relationships when there are two-way dependencies in the gene expression matrix (the gene-wise and experiment-wise dependencies). The main aspect of the framework is the use of a Kronccker product covariance matrix to model the gene-experiment interactions. The resulting novel gene coexpression measure, named Knorm correlation, can be understood as a natural extension of the widely used Pearson coefficient when the experiment correlation matrix is known. Compared with the Pearson coefficient, the Knorm correlation has a smaller estimation variance. The Knorm is also asymptotically consistent with the Pearson coefficient. When the experiment correlation matrix is unknown, the Knorm correlation is computed based on the estimated experiment correlation matrix by an iterative estimation procedure. We demonstrate the advantages of the Knorm correlation in both simulation studies and real datasets. The Knorm correlation estimation procedure is implemented in an R package (Knorm) that is freely available from the Bioconductor website. [ABSTRACT FROM AUTHOR]

This article studies weighted, generalized, least squares estimators in simple linear regression with serially correlated errors. Closed-form expressions of weighted least squares estimators and variances are presented under some common stationary autocorrelation settings, a first-order autoregression and a first-order moving-average. These explicit expressions also have appealing applications, including an efficient weighted least squares computation method and a new sufficient and necessary condition on the equality of weighted least squares estimators and ordinary least squares estimators. [ABSTRACT FROM AUTHOR]

The paper employs data from 2884 matches in the English Football League Championship. It builds a model of determinants of attendance designed to yield results relevant to decision-taking at individual clubs. The model has two innovatory features. It controls for the market size of home and away teams precisely by including local population measures constructed from the application of GIS software and information on competition from other clubs. It incorporates these time-invariant covariates in a Hausman-Taylor random effects estimator to take explicit account of variables typically excluded in earlier studies based on fixed effects models. Unlike fixed effects results, Hausman-Taylor estimates permit assessment of the role of market size and quality of the playing squad in determining attendance. Results also quantify the reduction in attendance from televising a match and show that attendance diminishes when a match is played simultaneously with a televised game in a higher status competition. [ABSTRACT FROM AUTHOR]

In a prospective cohort study, information on clinical parameters, tests, and molecular markers often is collected. Such information is useful to predict patient prognosis and to select patients for targeted therapy. We propose a new graphical approach, the positive predictive value (PPV) curve, to quantify the predictive accuracy of prognostic markers measured on a continuous scale with censored failure time outcome. The proposed method highlights the need to consider both predictive values and the marker distribution in the population when evaluating a marker, and it provides a common scale for comparing different markers. We consider both semiparametric- and nonparametric- based estimating procedures. In addition, we provide asymptotic distribution theory and resampling-based procedures for making statistical inference. We illustrate our approach with numerical studies and data sets from the Seattle Heart Failure Study. [ABSTRACT FROM AUTHOR]

We study the problem of analyzing and classifying human gait by modeling it as a stochastic process on a shape space. We consider gait as a evolution of human silhouettes as seen in video sequences, and focus on their shapes. More specifically, we define a shape space of planar, closed curves and model a human gait as a stochastic process on this space. Due to the periodic nature of human walk, this process is naturally constrained to be cyclostationary, that is, its mean path is assumed to be cyclic. We compare two subjects using a metric that quantifies differences between average gait cycles of each subject. This computation uses several tools from differential geometry of the shape space, including computation of geodesics, estimation of means of observed shapes, interpolation between observed shapes, and temporal registration of two gait cycles. Finally, we apply a nearest-neighbor classifier, using the gait metric, to perform human recognition, and present results from an experiment involving 26 subjects. [ABSTRACT FROM AUTHOR]

Percentiles (or quantiles) are ubiquitous in descriptive as well as inferential analyses of data. Many applications in practice involve percentiles from the normal distribution. We consider confidence interval estimation of a normal distribution percentile and study several methods including the ones based on the maximum likelihood and the approximate normality of sample percentiles, that is, order statistics. The nonparametric confidence interval, based on the sign test, is included as a bench- mark as it is a simple method and is valid for all continuous distributions. A Bayesian posterior predictive interval is also considered. The performance of the methods is examined in a simulation study via coverage and expected length. Summary and recommendations are given. [ABSTRACT FROM AUTHOR]

This article reviews Albert Einstein's first published paper, submitted for publication in 1900. At that time, Einstein was 21 and a recent college graduate. His paper uses modeling and least squares to analyze data in support of a scientific proposition. Einstein is shown to be well trained, for his day, in using statistics as a tool in his scientific research. This paper also shows his ability to make trivial arithmetic mistakes and some clumsiness in data recording. A major aim of this article is to help provide a better appreciation of Einstein as an active user of statistical arguments in this and other of his important publications. [ABSTRACT FROM AUTHOR]

Restricting the randomization of hard-to-change factors in industrial experiments is often required, resulting in a split-plot design structure. From an economic perspective, these designs minimize the experimental cost by reducing the number of resets of the hard-to-change factors. In this paper, unbalanced designs are considered for cases where the subplots are relatively expensive and the experimental apparatus accommodates an unequal number of runs per whole plot. We provide construction methods for unbalanced second-order split-plot designs that possess the equivalent estimation optimality property, providing best linear unbiased estimates of the parameters, independent of the variance components. Unbalanced versions of the central composite and Box-Behnken designs are developed. For cases where the subplot cost approaches the whole-plot cost, minimal point designs are proposed and illustrated with a split-plot Notz design. [ABSTRACT FROM AUTHOR]

In this study, the authors assess several strategies created on the basis of the Mantel-Haenszel (MH) procedure for conducting differential item functioning (DIF) analysis with small samples. One of the analytical strategies is a loss function (LF) that uses empirical Bayes Mantel-Haenszel estimators, whereas the other strategies use the classical MH statistics (the MH chisquare statistic using high levels of significance [0.20] or empirical criteria on the basis of the magnitude of the MH-delta estimator). The authors conducted a series of computer simulations in which they manipulated different types of tests, sample sizes, and ability distributions. The results show that the loss function does not offer advantages, in terms of power and Type I error rate, over other analytical strategies that use the classical MH statistics. [ABSTRACT FROM AUTHOR]

The classical variogram estimate is convenient but can be unacceptably variable. Improved estimators are possible, especially when the locations of the available data are highly clustered. Using a simple theoretical example, we demonstrate that weighting can dramatically increase the efficiency of classical variogram estimates from clustered data. We give expressions for the weights that lead to minimal variance estimators and indicate some obstacles to the use of these weights. We then introduce a simple iterative weighting scheme intended to approximate optimal weighting. We apply the new weighting to the example that motivated this research—estimating the variogram of home radon levels—and demonstrate its performance in a simulation study. [ABSTRACT FROM AUTHOR]

Sufficient dimension-reduction methods provide effective ways to visualize discriminant analysis problems. For example, Cook and Yin showed that the dimension-reduction method of sliced average variance estimation (SAVE) identifies variates that are equivalent to a quadratic discriminant analysis (QDA) solution. This article makes this connection explicit to motivate the use of SAVE variates in exploratory graphics for discriminant analysis. Classification can then be based on the SAVE variates using a suitable distance measure, If the chosen measure is Mahalanobis distance, then classification is identical to QDA using the original variables. Just as canonical variates provide a useful way to visualize linear discriminant analysis (LDA), so do SAVE variates help visualize QDA. This would appear to be particularly useful given the lack of graphical tools for QDA in current software. Furthermore, whereas LDA and QDA can be sensitive to nonnormality, SAVE is more robust. [ABSTRACT FROM AUTHOR]

Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the Savage representation. Examples of scoring rules for probabilistic forecasts in the form of predictive densities include the logarithmic, spherical, pseudospherical, and quadratic scores. The continuous ranked probability score applies to probabilistic forecasts that take the form of predictive cumulative distribution functions. It generalizes the absolute error and forms a special case of a new and very general type of score, the energy score. Like many other scoring rotes, the energy score admits a kernel representation in terms of negative definite functions, with links to inequalities of Hoeffding type, in both univariate and multivariate settings. Proper scoring ores for quantile and interval forecasts arc also discussed. We relate proper scoring rules to Bayes factors and to cross-validation. and propose a novel form of cross-validation known as random-fold cross-validation. A case study on probabilistic weather forecasts in the North American Pacific Northwest illustrates the importance of propriety. We note optimum score approaches to point and quantile estimation, and propose the intuitively appealing interval score as a utility function in interval estimation that addresses width as well as coverage. [ABSTRACT FROM AUTHOR]

Microarray technology allows a scientist to study genomewide patterns of gene expression. Thousands of individual genes are measured with a relatively small number of replications, which poses challenges to traditional statistical methods. In particular, the gone-specific estimators of variances are not reliable and gene-by-gene tests have low powers. In this article we propose a family of shrinkage estimators for variances raised to a fixed power. We derive optimal shrinkage parameters under both Stein and squared loss functions. Our results show that the standard sample variance is inadmissible under either loss function. We propose several estimators for the optimal shrinkage parameters and investigate their asymptotic properties under two scenarios: large number of replications and large number of genes. We conduct simulations to evaluate the finite sample performance of the data-driven optimal shrinkage estimators and compare them with some existing methods. We construct F-like statistics using these shrinkage variance estimators and apply them to detect differentially expressed genes in a microarray experiment. We also conduct simulations to evaluate performance of these F-like statistics and compare them with some existing methods. [ABSTRACT FROM AUTHOR]

Recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables (IVs) for causal inference. A basic idea is that IVs serve as an experimental handle, the turning of which may change each individual's treatment status and, through and only through this effect, also change observed outcome. The average difference in observed outcome relative to that in treatment status gives the average treatment effect for those whose treatment status is changed in this hypothetical experiment. We build on the modern IV framework and develop two estimation methods in parallel to regression adjustment and propensity score weighting in the case of treatment selection based on covariates. The IV assumptions are made explicitly conditional on covariates to allow for the fact that instruments can be related to these background variables. The regression method focuses on the relationship between responses (observed outcome and treatment status jointly) and instruments adjusted for covariates. The weighting method focuses on the relationship between instruments and covariates to balance different instrument groups with respect to covariates. For both methods, modeling assumptions are made directly on observed data and separated from the IV assumptions, whereas causal effects are inferred by combining observed-data models with the IV assumptions through identification results. This approach is straightforward and flexible enough to host various parametric and semiparametric techniques that attempt to learn associational relationships from observed data. We illustrate the methods by an application to estimating returns to education. [ABSTRACT FROM AUTHOR]

Control charts are powerful tools used to monitor the quality of processes. In practice, control chart limits are often calculated using parameter estimates from an in-control Phase I reference sample. In Phase II of the monitoring scheme, statistics based on new samples are compared with the estimated control limits to monitor for departures from the in-control state. Many studies that evaluate control chart performance in Phase II rely on the assumption that the in-control parameters are known. Although the additional variability introduced into the monitoring scheme through parameter estimation is known to affect the chart performance, many studies do not consider the effect of estimation on the performance of the chart. This paper contains a review of the literature that explicitly considers the effect of parameter estimation on control chart properties. Some recommendations are made and future research ideas in this area are provided. [ABSTRACT FROM AUTHOR]

Estimation of the survival curve for independently right-censored bivariate failure time data is a problem that has been studied extensively over the past 20 years. In this article we propose a new class of estimators for the bivariate survivor function based on locally efficient (LE) estimation. The LE estimator takes bivariate estimators Fn and Gn of the distributions of the time variables (T1, T2) and the censoring variables (C1, C2), and maps them to the resulting estimator ŜLE• If Fn and Gn are appropriate consistent estimators of F and G, then ŜLE will be nonparametrically efficient (thus the term "locally efficient"). However, if either Fn or Gn (but not both) is not a consistent estimator of F or G, then ŜLE will still be consistent and asymptotically normally distributed. We propose a locally efficient estimator that uses a consistent, nonparametric estimator for G and allows the user to supply lower-dimensional (semiparametric or parametric) working model for F. Because the estimator that we choose for G is consistent, the resulting LE estimator will always be consistent and c normal, and our simulation studies have indicated that using a lower-dimensional model for F gives excellent small-sample performance. In addition, our algorithm for calculation of the efficient influence curve at true distributions for F and G computes the efficiency bound for the model that can be used to calculate relative efficiencies for any bivariate estimator. In this article we introduce the LE estimator for bivariate right-censored data, present an asymptotic result, present the results of simulation studies, and perform a brief data analysis illustrating the use of the LE estimator. [ABSTRACT FROM AUTHOR]

In this article we consider three nonparametric maximum likelihood estimators based on mixed-case interval-censored data. Apart from the unrestricted estimator, we consider estimators under the assumption that the underlying distribution function of event times is concave or unimodal. Characterizations of the estimates are derived, and algorithms are proposed for their computation. The estimators are shown to be asymptotically consistent, and the benefits of additional constraints are illustrated through simulations. Finally, the estimators are used as an ingredient in a nonparametric comparison of two samples. [ABSTRACT FROM AUTHOR]

Under independent censoring, estimation of the covariate effects in the accelerated lifetime model may be based on censored data rank tests. Similar rank methodology has been developed with bivariate accelerated lifetime models for dependent censoring but uses artificial censoring, which may lead to substantial information loss. We present a new artificial censoring technique using pairwise ranking and establish the asymptotic properties of a pairwise rank estimator. Simulations show that the pairwise approach achieves large reductions in artificial censoring and large efficiency gains over the existing rank estimator. The simulations evidence moderate efficiency gains under independent censoring over a rank estimator that is semiparametric efficient under independent censoring. An AIDS data analysis illustrates the practical utility of the inferential procedures. [ABSTRACT FROM AUTHOR]

Case-control studies are among the most commonly used means of assessing association between exposure and outcome. Sample size determination and the optimal control-to-case ratio are vital to the design of such studies. In this article we investigate Bayesian sample size determination and the control-to-case ratio for case-control studies, when interval estimation is the goal of the eventual statistical analysis. In certain cases we are able to derive approximate closed-form sample size formulas. We also describe two Monte Carlo methods, each of which provides a unified approach to the sample size problem, because they may be applied to a wide range of interval-based criteria. We compare the accuracy of the different methods. We also extend our methods to include cross-sectional designs and designs for gene-environment interaction studies. [ABSTRACT FROM AUTHOR]

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiologic studies. In this article we propose a new class of semiparametric normal transformation models for right-censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivari- ate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonpara- metric maximum likelihood estimation in such models is practically prohibited due to the high-dimensional intractable integration of the likelihood function and the infinite-dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Asthma Study, and its performance is evaluated using simulations. [ABSTRACT FROM AUTHOR]

In this article we introduce a general methodology for producing a model-assisted empirical best predictor (EBP) of a finite population domain mean using data from a complex survey. Our method improves on the commonly used design-consistent survey estimator by using a suitable mixed model. Such a model combines information from related sources, such as census and administrative data. Unlike a purely model-based EBP, the proposed model-assisted EBP converges in probability to the customary design-consistent estimator as the domain and sample sizes increase. The convergence in probability is shown to hold with respect to the sampling design, irrespective of the assumed mixed model, a property commonly known as design consistency. This property ensures robustness of the proposed predictor against possible model failures. In addition, the convergence in probability is shown to be valid with respect to the assumed mixed model (model consistency). A new mean squared prediction error (MSPE) estimator is proposed. Unlike earlier MSPE estimators, our MSPE estimator is second-order unbiased. Our simulation results demonstrate the robustness properties of our proposed model-assisted predictor and the usefulness of the second-order unbiased MSPE estimator. [ABSTRACT FROM AUTHOR]

two-phase sampling, the second-phase sample is often a stratified sample based on the information observed in the first-phase sample. For the total of a population characteristic, either the double-expansion estimator or the reweighted expansion estimator can be used. Given a consistent first-phase replication variance estimator, we propose a consistent variance estimator that is applicable to both the double-expansion estimator and the reweighted expansion estimator. The proposed method can be extended to multiphase sampling. [ABSTRACT FROM AUTHOR]

Mixed linear models are used to analyze data in many settings. These models have a multivariate normal formulation in most cases. The maximum likelihood estimator (MLE) or the residual MLE (REML) is usually chosen to estimate the parameters. However, the latter are based on the strong assumption of exact multivariate normality. Welsh and Richardson have shown that these estimators are not robust to small deviations from multivariate normality. This means that in practice a small proportion of data (even only one) can drive the value of the estimates on their own. Because the model is multivariate, we propose a high-breakdown robust estimator for very general mixed linear models that include, for example, covariates. This robust estimator belongs to the class of S-estimators, from which we can derive asymptotic properties for inference. We also use it as a diagnostic tool to detect outlying subjects. We discuss the advantages of this estimator compared with other robust estimators proposed previously and illustrate its performance with simulation studies and analysis of three datasets. We also consider robust inference for multivariate hypotheses as an alternative to the classical F-test by using a robust score-type test statistic proposed by Heritier and Ronchetti, and study its properties through simulations and analysis of real data. [ABSTRACT FROM AUTHOR]

In this article we characterize all two-parameter count distributions (satisfying very general conditions) that are partially closed under addition. We also find those for which the maximum likelihood estimator of the population mean is the sample mean. Mixed Poisson models satisfying these properties are completely determined. Among these models are the negative binomial, Poisson-inverse Gaussian, and other known distributions. New count distributions can also be constructed using these characterizations. Three examples of application are given. [ABSTRACT FROM AUTHOR]

This article considers the analysis of clustered data via partial linear regression models. Adopting the idea of modeling the within-cluster correlation from the method of generalized estimating equations, a least squares type estimate of the slope parameter is obtained through piecewise local polynomial approximation of the nonparametric component. This slope estimate has several advantages: (a) It attains n1/2-consistency without undersmoothing; (b) it is efficient when correct within-cluster correlation is used, assuming multivariate normality of the error; (c) the preceding properties hold regardless of whether or not the nonparametric component is of cluster level; and (d) this estimation method naturally extends to deal with generalized partial linear models. Simulation studies and a real example are presented in support of the theory. [ABSTRACT FROM AUTHOR]

Based on one observation X from a N(θ, θ) distribution where θ(> 0) is an unknown parameter, this article provides an exact expression of the minimum variance unbiased estimator of θ based on the complete and sufficient statistic ∣X∣. Even though N(θ, θ) belongs to a one-parameter exponential family, I discuss some small surprises and intricacies that are worth noting. [ABSTRACT FROM AUTHOR]

Restricted maximum likelihood (REML) estimation of the parameters of the mixed model has become commonplace, even becoming the default option in many statistical software packages. However, a review of the literature indicates a need to update and clarify model selection techniques under REML, as ambiguities exist on the appropriateness of existing information criteria in this setting. A simulation study as well as an application assisted in gaining an understanding of the performance of information criteria in selecting the best model when using REML estimation. [ABSTRACT FROM AUTHOR]

As spatial autocorrelation latent in georeferenced data increases, the amount of duplicate information contained in these data also increases. This property suggests the research question asking what the number of independent observations, say , is that is equivalent to the sample size, n, of a data set. This is the notion of effective sample size. Intuitively speaking, when zero spatial autocorrelation prevails, ; when perfect positive spatial autocorrelation prevails in a univariate regional mean problem, . Equations are presented for estimating based on the sampling distribution of a sample mean or sample correlation coefficient with the goal of obtaining some predetermined level of precision, using the following spatial statistical model specifications: (1) simultaneous autoregressive, (2) geostatistical semivariogram, and (3) spatial filter. These equations are evaluated with simulation experiments and are illustrated with selected empirical examples found in the literature. [ABSTRACT FROM AUTHOR]

It is a common practice in finance to estimate volatility from the sum of frequently sampled squared returns. However, market microstructure poses challenges to this estimation approach, as evidenced by recent empirical studies in finance. The present work attempts to lay out theoretical grounds that reconcile continuous-time modeling and discrete-time samples. We propose an estimation approach that takes advantage of the rich sources in tick-by-tick data while preserving the continuous-time assumption on the underlying returns. Under our framework, it becomes clear why and where the "usual" volatility estimator fails when the returns are sampled at the highest frequencies. If the noise is asymptotically small, our work provides a way of finding the optimal sampling frequency. A better approach, the "two-scales estimator;' works for any size of the noise. [ABSTRACT FROM AUTHOR]

This article studies the estimation of conditional quantiles of counts. Given the discreteness of the data, some smoothness must be artificially imposed on the problem. We show that it is possible to smooth the data in a way that allows inference to be performed using standard quantile regression techniques. The performance and implementation of the estimators are illustrated by simulations and an application. [ABSTRACT FROM AUTHOR]

In this article we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear models (GPLMs) for longitudinal data or clustered data in general. We approximate the nonparametric function in the GPLM by a regression spline, and use bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers. We show that the regression spline approach avoids some of the intricacies associated with the profile-kernel method, and that robust estimation and inference can be carried out operationally as if a generalized linear model were used. [ABSTRACT FROM AUTHOR]