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Quantile regression is a technique to estimate the conditional quantile. In this paper we propose a localized method for quantile regression, the regularized moving quantile regression, which can be used to analyze scattered data efficiently. We present a rigorous global error analysis in the learning theory framework. The main results include an inequality that bridges the gap between the global risk and local risk, a characterization of the approximation that shows the moving technique allows to approximate very complicated functions by simple function classes, and a learning rate analysis. These results indicate that the moving quantile regression method converges fast under mild conditions. • We establish a relationship between the local risk and global risk. • We introduce a novel assumption to characterize the approximation ability. • We derive an explicit learning rate for the moving quantile regression. [ABSTRACT FROM AUTHOR]

Abstract Motivated by an application in the context of experimental fatigue tests we study the problem of estimating conditional quantiles from data that contains additional measurement errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We show that the plug-in quantile estimate corresponding to a local averaging estimate of the conditional distribution function (codf) approaches the quantile set asymptotically, presumed that the local averaging estimate of the codf is pointwise strongly consistent. We also investigate the rate of convergence and show that our plug-in estimate achieves at least the same pointwise rate of convergence as the local averaging estimate of the codf plus the square root of the weighted sum of the absolute errors. Finally, the results are applied in simulations and in the context of experimental fatigue tests. Highlights • Nonparametric quantile estimation of number of cycles in experimental fatigue tests. • Consistency result for quantile estimate based on data with measurement errors (ME). • Proof of rate of convergence for this quantile estimate based on data with ME. [ABSTRACT FROM AUTHOR]

Abstract This paper considers the problem of simultaneous testing of multiple hypotheses in a multi-stage group sequential setting subject to control over the false discovery rate (FDR). A multi-stage group sequential form of the BH procedure is developed, and a proof of its FDR control for p -values satisfying a positive dependence condition both between and within stages is given. This group sequential BH is adapted to the proportion of true nulls in two different ways, resulting in the proposal of two adaptive group sequential BH. While one of these adaptive procedures is theoretically shown to control its FDR when the p -values are positively dependent between but independent within stages, the other one's FDR control is assessed through simulations. Comparative performance studies of the proposed procedures in terms of FDR control, power, and proportion of sample saved carried out through extensive simulations provide evidence of superior performance of the proposed adaptive procedures. Highlights • BH method is extended from single to multiple stages in a group sequential setting. • Error spending function is used to allocate a nominal level for the FDR control at each stage. • The group sequential BH controls FDR under positive dependence both within and between stages. • Two different adaptive versions of group sequential BH are given. [ABSTRACT FROM AUTHOR]

Abstract In many empirical situations, modelling simultaneously three or more outcomes as well as their dependence structure can be of considerable relevance. Copulae provide a powerful framework to build multivariate distributions and allow one to view the specification of the marginal responses' equations and their dependence as separate but related issues. We propose a generalizationof the trivariate additive probit model where the link functions can in principle be derived from any parametric distribution and the parameters describing the residual association between the responses can be made dependent on several types of covariate effects (such as linear, nonlinear, random, and spatial effects). All the coefficients of the model are estimated simultaneously within a penalized likelihood framework that uses a trust region algorithm with integrated automatic multiple smoothing parameter selection. The effectiveness of the model is assessed in simulation as well as empirically by modelling jointly three adverse birth binary outcomes in North Carolina. The approach can be easily employed via the gjrm() function in the R package GJRM. Highlights • Development of trivariate binary models with arbitrary link functions. • The correlation parameters are allowed to depend upon covariates. • The models allow spline-type structures to capture nonlinear relationships. • The above developments are available via the gjrm() function from the R package GJRM. [ABSTRACT FROM AUTHOR]

Abstract Initial screening experiments often leave some problems unresolved, adding follow-up runs is needed to clarify the initial results. In this paper, a technique is developed to add additional experimental runs to an initial supersaturated design. The added runs are generated with respect to the Bayesian D s -optimality criterion and the procedure can incorporate the model information from the initial design. After analysis of the initial experiment with several methods, factors are classified into three groups: primary, secondary, and potential according to the times that they have been identified. The focus is on those secondary factors since they have been identified several times but not so many that experimenters are sure that they are active, the proposed Bayesian D s -optimal augmented design would minimize the error variances of the parameter estimators of secondary factors. In addition, a blocking factor will be involved to describe the mean shift between two stages. Simulation results show that the method performs very well in certain settings. Highlights • Bayesian D s -optimal augmented SSD uses initial-design info to plan follow-up runs. • The factor classification is determined by multiple analysis methods. • The new method considers the shift in average responses between the two experiments. • The Bayesian D s -optimality performs better in certain situations. [ABSTRACT FROM AUTHOR]

Abstract The aim of this paper is twofold. First a new imperfect maintenance model is introduced. This model is an extension of Finkelstein's Geometric Failure Rate Reduction model, using the modification proposed by Bordes and Mercier for extending the Geometric Process. Second, based on the observation of several systems, the semiparametric inference in this model is studied. Estimators of the euclidean and functional model parameters are derived and their asymptotic normality is proved. A simulation study is carried out to assess the behavior of these estimators for samples of small or moderate size. Finally, an application on a real dataset is presented. Highlights • A new imperfect maintenance model is introduced. • This model is an extension of Finkelstein's Geometric Failure Rate Reduction model. • The semiparametric inference in this model is studied. • Estimators of the model parameters are derived, their asymptotic normality is proved. • A simulation study is carried out to assess the behavior of these estimators. • An application on a real dataset is presented. [ABSTRACT FROM AUTHOR]

Abstract We study the asymptotic behavior of Bayes-type estimators and give sufficient conditions to obtain the asymptotic limit distribution of the estimation error. We assume so called polynomial-type large deviation inequalities and prove the asymptotic equivalence of the estimation errors of Bayes-type and M-estimators by virtue of Ibragimov–Has'minskiĭ theory. The results can be applied to several cases such as diffusion processes and jump diffusion processes. In this paper, we focus on the application to ergodic diffusion processes and ergodic jump diffusion processes, demonstrating asymptotic normality and convergence of moments for Bayes-type estimators with general loss functions. [ABSTRACT FROM AUTHOR]

Abstract We study the consistency of the standard (non-parametric) bootstrap, the m -out-of- n bootstrap, and the oracle bootstrap distributions of some popular LASSO-type estimators in regression models with random predictors. These estimators have an oracle property and are often used in estimation of sparse regression models. A local asymptotic analysis further reveals the behavior of these estimators and of their bootstrap distributions when some regression coefficients approach zero at various rates. In a simulation study, we assess the finite sample properties of the estimators and of their bootstrap distributions for various sample sizes and model parameters. The analysis of a prostate cancer data set shows an application of LASSO-type inference and bootstrap methods in practice. Highlights • Large sample local behavior of the Bridge and ALASSO estimators in linear regression models. • Large sample local behavior of the substitution and plug-in standard bootstrap distributions of the Bridge and ALASSO estimators. • Large sample local behavior of the m-out-of-n bootstrap distributions of the Bridge and ALASSO estimators. • Large sample local behavior of the oracle bootstrap distributions of the Bridge and ALASSO estimators. [ABSTRACT FROM AUTHOR]

Abstract The evaluation of a set of objects, e.g. items of a production lot, in terms of a random measurement, such that the decision is statistically designed to control the probability of false decisions considered as a function of the fraction of measurements falling below a threshold, can be conducted by acceptance sampling procedures. These methods are typically studied for the quality control problem to accept or reject a lot of produced items. This paper provides an extension of the acceptance sampling methodology to a multi-stage framework where a lot is inspected at several time points and only accepted if it passes all stages. The resulting sampling plans allow to specify both the stage-wise and overall error probabilities and can be calculated before inspections start. Going beyond the case of independent random samples drawn at each inspection time, we consider a panel type design resulting in a dependent sampling scheme. Based on asymptotic approximations we provide explicit formulas for the proposed sampling plans and an effective recursive algorithm for their calculation. The theoretical results cover consistency and asymptotic optimality of the sampling plans as well as a central limit theorem. The statistical properties of the approach are studied by simulations. Highlights • Extension of Acceptance Sampling to Multiple Stages. • Asymptotically Optimal Sample Sizes. • Dependent Panel-type Sampling Design. • Numerical Determination of Optimal Weights. • Extensive Simulation Study. [ABSTRACT FROM AUTHOR]

Abstract In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple selection algorithm. We compute exactly the variance of linear estimators constructed upon these designs by using the first and second order inclusion probabilities. Moreover, we obtain asymptotic and finite sample theorems. We construct explicitly fixed size determinantal sampling designs with given first order inclusion probabilities. We also address the search of optimal determinantal sampling designs. Highlights • We study a new class of sampling designs: determinantal sampling designs (DSDs). • We compute exactly the variance of linear estimators constructed upon these designs. • We obtain asymptotic and finite distance theorems. • We construct explicitly fixed size DSDs with given first order inclusion probabilities. • We also address the search of optimal DSDs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the adequacy check of the varying-coefficient model when covariates are measured with error and some auxiliary variable is available. With the help of auxiliary variable, we calibrate the measurement error and obtain an estimator of the unobservable true variable. The empirical-process-based test is built by applying the calibrated estimator of the model error. The asymptotic properties of the proposed test are rigorously investigated under the null hypothesis, local and global alternatives. It is shown that the proposed test is consistent and has good properties of power. We illustrate that the naive method cannot control Type I error and loses effect completely. But the proposed calibrated method performs well in terms of the empirical sizes close to the test level and high empirical powers. Simulation studies and two real data analyses are conducted to demonstrate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Complex Ornstein–Uhlenbeck (OU) processes have various applications in statistical modelling. They play role e.g. in the description of the motion of a charged test particle in a constant magnetic field or in the study of rotating waves in time-dependent reaction diffusion systems, whereas Kolmogorov used such a process to model the so-called Chandler wobble, small deviation in the Earth’s axis of rotation. In these applications parameter estimation and model fitting is based on discrete observations of the underlying stochastic process, however, the accuracy of the estimation strongly depend on the observation points. This paper studies the properties of D-optimal designs for estimating the parameters of a complex OU process with a trend. In special situations we show that in contrast with the case of the classical real OU process, a D-optimal design exists not only for the trend parameter, but also for joint estimation of the covariance parameters, moreover, these optimal designs are equidistant. [ABSTRACT FROM AUTHOR]

While the statistical inference of Vasicek processes driven by both Brownian motions and fractional Brownian motions has a long history, the statistical analysis for the Vasicek model driven by other fractional Gaussian processes is obviously more recent. This paper considers the parameter estimation problem for Vasicek processes driven by sub-fractional Brownian motions with the known Hurst parameter greater than one half. Since the maximum likelihood estimators are hardly analyzed because of the stochastic integrals with singular kernels, least squares estimators for drift parameters are provided based on time-continuous observations. The strong consistency results as well as the asymptotic distributions of these estimators are obtained in both the non-ergodic case and the null recurrent case. [ABSTRACT FROM AUTHOR]

A general result is derived on the finite-sample approximate bias of the Gaussian maximum likelihood estimator of the full vector of parameters in ARMA models when the error term may be nonnormally distributed and exogenous regressors may be included. It is found that there is typically estimation bias for parameters associated with the AR and MA terms and the bias depends only on these parameters themselves and the exogenous regressors. Parameters associated with the exogenous regressors are estimated approximately unbiased. The error variance is estimated with a downward bias, proportional to the number of exogenous regressors and the orders of AR and MA terms in the model. The distributional assumption on the error term does not affect the general bias result. Monte Carlo experiments are provided to illustrate the effectiveness of using analytical bias for the purpose of bias correction. [ABSTRACT FROM AUTHOR]

Through investigating a recently introduced sufficient dimension reduction method with Hellinger index, this article shows that the generalized Hellinger index unifies three existing dimension reduction methods: kernel discriminant analysis, sliced regression and density minimum average variance estimation, with certain weight functions. The Hellinger index is then extended to regression models with multivariate responses. Furthermore, new algorithms based on Hellinger index to estimate the dual central subspaces and to enable variable selection for sparse models are proposed. Simulation studies and a real data analysis demonstrate the efficacy of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a tilted estimator for nonparametric estimation of a density function. We use a cross-validation criterion to choose both the bandwidth and the tilted estimator parameters. We demonstrate theoretically that our proposed estimator provides a convergence rate which is strictly faster than the usual rate attained using a conventional kernel estimator with a positive kernel. We investigate the performance through both theoretical and numerical studies. [ABSTRACT FROM AUTHOR]

This paper provides new insights into coding invariance for linear models with qualitative factors, including a coding invariant way of denoting the model coefficients. On this basis, “interaction contributions” (ICs) are proposed for decomposing generalized word counts for factorial designs into contributions that neither depend on level allocation nor on the coding of factors. Combinatorially equivalent designs yield the same ICs, so that ICs are suitable for classifying factorial designs with qualitative factors. ICs are based on singular value decomposition and have an interpretation in terms of bias contributions of an interaction on the estimation of the overall mean. The paper introduces ICs and their tabulations in interaction contribution frequency tables and illustrates their behavior in various examples. ICs are compared to several other tools for assessing combinatorial equivalence of general factorial designs, and they are found to provide a useful complement to existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of multiplicative models with a single-index structure called single-index multiplicative models, which greatly extend the range of application of positive response data since it allows the presence of nonparametric link and also mitigates the curse of dimensionality. Firstly, based on the least product relative error (LPRE) method proposed recently by Chen et al. (2016), we propose an iterative LPRE approach for estimation of parameters and nonparametric function, where a local kernel-weighted LPRE approach is developed. Under some regularity conditions, we prove that proposed estimates have nice asymptotic normalities for both nonparametric function and parameter vector. Secondly, to make inference on the parameter vector, an empirical likelihood procedure is presented, which facilitates confidence region construction without estimating covariance matrix. Finally, extensively numerical studies are carried out to evaluate the finite sample performance of proposed approaches. [ABSTRACT FROM AUTHOR]

In this article, we propose a focused information criterion (FIC) and develop a frequentist model averaging estimation procedure for a partial linear regression model when the response is randomly right-censored. The proposed procedure is based on the quantile regression and can depict the comprehensive character of the distribution of the response by means of modeling different quantiles. The large sample properties of the proposed estimators are established, and their finite sample properties are examined through simulation studies. An application to a primary biliary cirrhosis data set is provided. [ABSTRACT FROM AUTHOR]

High frequency based estimation methods for a semiparametric pure-jump subordinated Brownian motion exposed to a small additive microstructure noise are developed building on the two-scales realized variations approach originally developed by Zhang et al. (2005) for the estimation of the integrated variance of a continuous Itô process. The proposed estimators are shown to be robust against the noise and, surprisingly, to attain better rates of convergence than their precursors, method of moment estimators, even in the absence of microstructure noise . Our main results give approximate optimal values for the number K of regular sparse subsamples to be used, which is an important tune-up parameter of the method. Finally, a data-driven plug-in procedure is devised to implement the proposed estimators with the optimal K -value. The developed estimators exhibit superior performance as illustrated by Monte Carlo simulations and a real high-frequency data application. [ABSTRACT FROM AUTHOR]

In recent years, high-dimensional data has become increasingly prevalent with rapid development of data collecting technologies. Much work has been done for hypothesis testing on mean vectors, especially for high-dimensional two-sample problems. Rather than considering a specific problem, we are interested in a general linear hypothesis testing problem on mean vectors of several populations, which includes many existing hypotheses about mean vectors as its special cases. We propose a test statistic based on a linear combination of U-statistics which can be quickly calculated without using computationally intensive U-statistics. Asymptotic normality and power of our test are derived under mild conditions without requiring an explicit relation between the data dimension and the sample size. Our test is applicable to non-normal multi-sample high-dimensional data without assuming a common covariance matrix among different samples. It also works well even when different samples follow different distributions, provided that some moment conditions are satisfied. A simple, computationally-efficient, and ratio-consistent estimator of the unknown variance of our test statistic is also provided which is not based on U-statistic calculations. Simulation studies and a real data example are presented to demonstrate the good performance of our test. [ABSTRACT FROM AUTHOR]

We propose some backward–forward martingale decompositions for functions of reversible Markov chains. These decompositions are used to prove the functional Central limit theorem for reversible Markov chains with asymptotically linear variance of partial sums. We also provide a proof of the equivalence between asymptotic linearity of the variance and convergence of the integral of 1 / ( 1 − t ) with respect to the associated spectral measure ρ . We show a result on uniform integrability of the supremum of the average sum of squares of martingale differences. We also study the asymptotic behavior of linear processes having as innovations mean zero square integrable functions of stationary reversible Markov chains. We include in our study the long-range dependence case. We apply this study to several cases of reversible stationary Markov chains that arise in regression estimation. [ABSTRACT FROM AUTHOR]

It is known that a statistically significant treatment may not be clinically significant. A quantity that can be used to assess clinical significance is called the minimum clinically important difference (MCID), and inference on the MCID is an important and challenging problem. Modeling for the purpose of inference on the MCID is non-trivial, and concerns about bias from a misspecified parametric model or inefficiency from a nonparametric model motivate an alternative approach to balance robustness and efficiency. In particular, a recently proposed representation of the MCID as the minimizer of a suitable risk function makes it possible to construct a Gibbs posterior distribution for the MCID without specifying a model. We establish the posterior convergence rate and show, numerically, that an appropriately scaled version of this Gibbs posterior yields interval estimates for the MCID which are both valid and efficient even for relatively small sample sizes. [ABSTRACT FROM AUTHOR]

We consider a single-index quantile regression model for longitudinal data. Based on generalized estimating equations, an estimation procedure is proposed by taking into account the correlation within subject. Under mild assumptions, we derive the convergence rate of the estimator of the unknown link function and the asymptotic normality of estimator of the index parameter using the “projection” technique. Since the estimating equations are non-continuous, we further adopt the smoothing approach and show that estimators obtained from the smoothed estimating equations are asymptotically equivalent to that from the unsmoothed estimating equations. It is also shown that the estimator is more efficient when the correlation is correctly specified. Finally, we present numerical examples including simulations and analysis of a lung function data. [ABSTRACT FROM AUTHOR]

We consider the estimation for the unknown single-index parameter in the conditional density function. Firstly, estimation method and asymptotic properties for the estimator are obtained. Secondly, to test a hypothesis on the single-index parameter, a test statistic based on the difference between the minimization criteria under the null and alternative hypotheses is proposed. We show that the limiting distribution for the test statistics is a weighted sum of independent standard chi-squared distributions. Besides, a local alternative hypothesis that converges to the null hypothesis at an n − 1 / 2 rate is also considered. A bootstrap procedure is proposed to calculate critical values. Finally, simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed as an illustration. [ABSTRACT FROM AUTHOR]

This paper proposes an M -estimator for the fractional parameter of stationary long-range dependent processes as an alternative to the classical GPH (Geweke and Porter-Hudak, 1983) method. Under very general assumptions on the long-range dependent process the consistency and the asymptotic normal distribution are established for the proposed method. One of the main results is that the convergence rate of the M -estimator is N β / 2 , for some positive β , which is the same rate as the standard GPH estimator. The asymptotic properties of the M -estimation method is investigated through Monte-Carlo simulations under the scenarios of ARFIMA models using contaminated with additive outliers and outlier-free data. The GPH approach is also considered in the study for comparison purposes, since this method is widely used in the literature of long-memory time series. The empirical investigation shows that M and GPH-estimator methods display standardized densities fairly close to the standard Gaussian density in the context of non-contaminated data. On the other hand, in the presence of additive outliers, the M -estimator remains unaffected with the presence of additive outliers while the GPH is totally corrupted, which was an expected performance of this estimator. Therefore, the M -estimator here proposed becomes an alternative method to estimate the long-memory parameter when dealing with long-memory time series with and without outliers. [ABSTRACT FROM AUTHOR]

This note highlights some unusual and unexpected behavior in point estimation using empirical likelihood (EL). In particular, frequency domain formulations of EL, based on the periodogram and estimating functions, have been proposed in the literature for time and spatial processes. However, in contrast to the time series case and most applications of EL, the maximum EL parameter estimator exhibits surprisingly non-standard asymptotic properties for irregularly located spatial data. In fact, a consistent normal limit cannot be guaranteed, as is typical for EL. Despite this, log-ratio EL statistics maintain standard chi-square limits with such spatial data. [ABSTRACT FROM AUTHOR]

This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a data-driven procedure using kernel rules. The bandwidth is selected using the approach of Goldenshluger and Lepski and we prove that the resulting estimator satisfies an oracle type inequality. The procedure is also proved to be adaptive (in a minimax framework) over a scale of Hölder balls for several types of dependence: strong mixing processes, λ -dependent processes or i.i.d. sequences can be considered using a single procedure of estimation. Some simulations illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In environmental studies, it is a common practice to follow the continuous-plane paradigm for estimating parameters of interest, like totals or means, of spatial variables defined over a surface whose points correspond to points of a connected and compact subset of R 2 . In the design-based approach, randomness comes from the random sampling of points in the domain, wherein to observe the values of the spatial variable. Adopting this type of approach, under a model-assisted framework, in this paper we present a class of estimators of the total of the spatial variable, which are based on linear mixed models. We introduce first the mixed model regression estimator of the total and its properties. Methods for choosing the smoothing parameter are also discussed. Then, we present the penalized splines regression estimator of the total, as a member of the class, and its asymptotic properties when the number of knots increases with the sample size within an infill asymptotic framework. This estimator, under mild conditions, is proved to be asymptotically unbiased, consistent, asymptotically normally distributed, and more efficient than the basic unbiased estimator. Furthermore, it can be super-efficient, that is, the variance order may be higher than the usual n − 1 , according to the degree of smoothness of the spatial variable. A simulation study shows the performance of the estimator as well as that of the proposed variance estimators. [ABSTRACT FROM AUTHOR]

We study in detail the bias and variance of the entropy estimator proposed by Kozachenko and Leonenko (1987) for a large class of densities on R d . We then use the work of Bickel and Breiman (1983) to prove a central limit theorem in dimensions 1 and 2 . In higher dimensions, we provide a development of the bias in terms of powers of N − 2 / d . This allows us to use a Richardson extrapolation to build, in any dimension, a root- n consistent entropy estimator satisfying a central limit theorem which allows for explicit (asymptotic) confidence intervals. To our knowledge, all the previous general root- n consistency results were concerning dimension 1 . [ABSTRACT FROM AUTHOR]

This paper is concerned with prediction for Gamma models, and more specifically the estimation of a predictive density for Y ∼ G a ( α 2 , β ) under Kullback–Leibler loss, based on X ∼ G a ( α 1 , β ) . The main focus pertains to situations where there is a parametric constraint of the form β ∈ C = ( a , b ) . We obtain representations for Bayes predictive densities and the minimum risk equivariant predictive density in the unconstrained problem. It is shown that the generalized Bayes estimator against the truncation of the non-informative prior onto C dominates the minimum risk equivariant predictive density and is minimax whenever a = 0 or b = ∞ . Analytical comparisons of plug-in predictive densities Ga ( α 2 , β ˆ ) , which include the predictive mle density, are obtained with results applying as well for point estimation under dual entropy loss β β ˆ − log ( β β ˆ ) − 1 . Numerical evaluations confirm that such predictive densities are much less efficient than some Bayesian alternatives in exploiting the parametric restriction. Finally, it is shown that variance expansion improvements of the form G a ( α 2 k , k β ˆ ) of plug-in predictive densities can always be found for a subset of k > 1 values and non-degenerate β ˆ . [ABSTRACT FROM AUTHOR]

Shared frailty models are frequently used for inducing dependence between survival times. In this paper, we consider bivariate current status data that are reasonable to model by shared frailty models. A time-dependent association measure that has a conditional probability interpretation is revisited for its potential application to such data. We propose a method of estimation and derive asymptotic standard errors for this measure. Its small sample performance and its performance in assessing the temporal variation in the strength of association in realistic scenarios is investigated by means of experiments. We show that the measure based on the conditional probability can vary with time even in the absence of any time-dependent effects. Furthermore, we give evidence that it lacks interpretability in suggesting appropriate frailty models. We provide an illustration with multivariate current status data arising from a community-based study of cardiovascular diseases in Taiwan. We compare the observed patterns of association with the ones obtained by employing a fairly new time-varying association measure that is relevant for shared frailty models, owing to its connection to the cross-ratio function, and which serves as a diagnostic tool for suggesting classes of frailty distributions with constant, increasing or decreasing association over time. [ABSTRACT FROM AUTHOR]

Two new orthogonally equivariant estimators of the covariance matrix are proposed. The estimates of the population eigenvalues are isotonized maximum likelihood estimates of the modified profile likelihood obtained from the Wishart distribution, in one case, and of a penalized form of such a likelihood function, in the other, with a penalty that constrains the trace of the sample covariance matrix. Properties of these estimators are studied and numerical risk comparisons with six other well-known estimators are presented to demonstrate the robustness of the proposed estimators for various real and simulated covariance structures. [ABSTRACT FROM AUTHOR]

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies. The proposed design and inference procedure is shown to be statistically more powerful than existing alternative designs with the same sample sizes. We illustrate the proposed method with an existing real data from the Cancer Incidence and Mortality of Uranium Miners Study. [ABSTRACT FROM AUTHOR]

A multivariate semiparametric partial linear model for both fixed and random design cases is considered. In either case, the model is analyzed using a difference sequence approach. The linear component is estimated based on the differences of observations and the functional component is estimated using a multivariate Nadaraya–Watson kernel smoother of the residuals of the linear fit. We show that both components can be asymptotically estimated as well as if the other component were known. The estimator of the linear component is shown to be asymptotically normal and efficient in the fixed design case if the length of the difference sequence used goes to infinity at a certain rate. The functional component estimator is shown to be rate optimal if the Lipschitz smoothness index exceeds half the dimensionality of the functional component argument. We also develop a test for linear combinations of regression coefficients whose asymptotic power does not depend on the functional component. All of the proposed procedures are easy to implement. Finally, numerical performance of all the procedures is studied using simulated data. [ABSTRACT FROM AUTHOR]

In order to construct prediction intervals without the cumbersome–and typically unjustifiable–assumption of Gaussianity, some form of resampling is necessary. The regression set-up has been well-studied in the literature but time series prediction faces additional difficulties. The paper at hand focuses on time series that can be modeled as linear, nonlinear or nonparametric autoregressions, and develops a coherent methodology for the construction of bootstrap prediction intervals. Forward and backward bootstrap methods using predictive and fitted residuals are introduced and compared. We present detailed algorithms for these different models and show that the bootstrap intervals manage to capture both sources of variability, namely the innovation error as well as estimation error. In simulations, we compare the prediction intervals associated with different methods in terms of their achieved coverage level and length of interval. [ABSTRACT FROM AUTHOR]

In dose–response studies, experiments are often carried out according to optimal designs for the purpose of accurately determining a specific effective dose (ED) level. If the interest is in the dose–response relationship over a range of ED levels, the existing optimal designs is misaligned. In this paper, we propose a two-stage sequential ED-design for this purpose. We use a small number of trials to provide a tentative estimation of the parameters. The dose levels of the subsequent trials are then selected sequentially, based on the latest model information, to maximize the efficiency of the ED estimation over several ED levels. Simulations indicate that the proposed design compares favorably with existing designs under various scenarios. [ABSTRACT FROM AUTHOR]

This paper considers an adaptive method based on relative error criteria to select grouped variables and estimate parameters simultaneously for the multiplicative regression model. The oracle properties of the proposed method are established. Simulation studies indicate that the proposed relative error approach has better performance to detect effective groups relative to several existing methods based on absolute error criteria, for example, the least squares and the least absolute deviation. Application is illustrated with the body fat and the birth weight datasets. [ABSTRACT FROM AUTHOR]

The estimation of covariance matrices is an important area in multivariate statistics and arises naturally in many applications. Stein’s covariance estimator is regarded as a benchmark in the literature, as it generally yields remarkable risk reductions compared to the maximum likelihood estimator (MLE) in small sample sizes. In its original or raw form, however, Stein’s estimator becomes unbounded when two sample eigenvalues approach each other. Thus, in some settings, Stein’s raw estimator has greater risk than the MLE. This implies that Stein’s raw estimator is not uniformly better than the MLE and thus cannot always be used as an alternative. The problem of the unbounded behavior of Stein’s raw estimator is often mitigated by employing an ad hoc isotonizing algorithm which has no formal statistical basis. By leveraging Stein’s unbiased estimator of risk framework, in this paper we propose a general approach that prevents the unbounded behavior of the unbiased estimator of risk as two sample eigenvalues approach each other. We then employ this framework to obtain a proof-of-concept for constructing covariance estimators which retain the attractive properties of Stein’s estimator and are simultaneously uniformly better than the MLE. [ABSTRACT FROM AUTHOR]

We investigate the large sample behavior of a p -value based procedure for estimating the threshold level at which a regression function takes off from its baseline value, a problem arising in dose–response studies, engineering and other related fields. We study the procedure under the “repeated measurement” setting, where several responses can be obtained at each covariate-level. The estimator is constructed via fitting a “stump” function to approximate p -values that test for deviation of the regression function from its baseline level. The smoothness of the regression function in the vicinity of the threshold determines the best possible rate of convergence using our method: a “cusp” of order k at the threshold yields a rate of N − 1 / ( 2 k + 1 ) , where N is the size/budget of the problem (total number of responses across all values of covariates). The asymptotic distribution of the normalized estimator is shown to be the minimizer of a generalized compound Poisson process and confidence intervals based on this distribution are proposed. The method is illustrated on simulations and an application to data from a complex queuing system is presented. [ABSTRACT FROM AUTHOR]

Starting from a real data example in fluorescence, the problem of nonparametric estimation of a density in a biased data model is considered. Bias correction can be done in two ways: either an estimator is computed with the data and in a second time a correction (plug in estimator) is applied, or weights are directly associated with the data so that a direct estimator of the quantity of interest (weighted estimator) is obtained. In both cases, kernel and projection estimation strategies with bandwidth or model selection devices are developed. The bandwidth selection is inspired from a procedure recently proposed by Goldenshluger and Lepski (2011). Risk bounds are proved showing that the final data-driven estimators perform an automatic finite sample bias–variance tradeoff. A simulation study compares the two bias-correction methods and the different model or bandwidth selection methods. Finally real fluorescence data are studied. [ABSTRACT FROM AUTHOR]

This paper proposes the nonnegative adaptive lasso method for variable selection both in the classical fixed p setting (OLS initial estimator) and the ultra-high dimensional setting (root-n-consistent initial estimator). This method is an extension of the adaptive lasso with nonnegative constraint on the coefficients. It is shown to have asymptotic unbiasedness, asymptotic normality and variable selection consistency and its mean squared error decays fast too. Comparing with other procedures, nonnegative adaptive lasso satisfies oracle properties and can select the true variables under fewer assumptions. To get the solution of the nonnegative adaptive lasso, we extend the multiplicative approach for computing. This algorithm is valid for the general framework where the number of regression parameters p is allowed to very large. Simulations are performed to illustrate above results. The constrained index tracking problem in the stock market without short sales is studied in the empirical part. A two-stage method, nonnegative adaptive lasso + nonnegative LS, is applied in the financial modeling. The tracking results indicate that nonnegative adaptive lasso and the two-stage method can both get small tracking error and is successful in assets selection. [ABSTRACT FROM AUTHOR]

Varying coefficient models are useful for modeling longitudinal data and have been extensively studied in the past decade. Motivated by commonly encountered dichotomous outcomes in medical and health cohort studies, we propose a two-step method to estimate the regression coefficient functions in a logistic varying coefficient model for a longitudinal binary outcome. The model depicts time-varying covariate effects without imposing stringent parametric assumptions. The proposed estimation is simple and can be conveniently implemented using existing statistical packages such as SAS and R. We study asymptotic properties of the proposed estimators which lead to asymptotic inference and also develop bootstrap inferential procedures to test whether the coefficient functions are indeed time-varying or are equal to zero. The proposed methodology is illustrated with the analysis of a smoking cessation data set. Simulations are used to evaluate the performance of the proposed method compared to an alternative estimation method based on local maximum likelihood. [ABSTRACT FROM AUTHOR]

Presmoothed Kaplan–Meier integrals have been proposed as suitable estimators in semiparametric censorship models. They are based on a modification of Kaplan–Meier weights which replaces the censoring indicators by some smooth (parametric) fit to the conditional probability of uncensoring, leading to estimators with smaller variance. In this paper an asymptotic representation of these estimators as a sum of i.i.d. random variables is established. The situation in which covariates are present is considered; therefore, the present paper extends previous results in Dikta et al. (2005) to the setting with covariates. As a consequence, a CLT for presmoothed Kaplan–Meier integrals with covariates is obtained. Application to censored regression is given. The finite sample performance of the estimator is investigated through simulations. [ABSTRACT FROM AUTHOR]

In many areas of science, models are used to describe attributes of complex systems. These models are generally themselves highly complex functions of their inputs, and can be computationally expensive to evaluate. Often, these models have parameters which must be estimated using data from the real system. In this paper, we address the problem of using prior information supplied by the model, in conjunction with prior beliefs about its parameters, to design the collection of data such that it is optimal for decisions which must be made using posterior beliefs about the model parameters. Optimal design calculations do not generally have a closed form solution, so we propose a Bayes linear analysis to find an approximately optimal design. We motivate the approach by considering optimal specification of measurement locations for remote sensing of airborne species. [ABSTRACT FROM AUTHOR]

High breakdown-point regression estimators protect against large errors and data contamination. We adapt and generalize the concept of trimming used by many of these robust estimators so that it can be employed in the context of the generalized method of moments. The proposed generalized method of trimmed moments (GMTM) offers a globally robust estimation approach (contrary to many existing locally robust estimators) applicable in models identified and estimated using moment conditions. We derive the consistency and asymptotic distribution of GMTM in a general setting, propose a robust test of overidentifying conditions, and demonstrate the application of GMTM in the instrumental variable regression. We also compare the finite-sample performance of GMTM and existing estimators by means of Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

We show some equalities for three estimators: (1) the ordinary least-squares estimators ( OLSE ), (2) the weighted least-squares estimators ( WLSE ), (3) the best linear unbiased estimator ( BLUE ) under the general growth curve model (A) μ 1 = { Y , X 1 Θ X 2 , σ 2 ( Σ 2 ⊗ Σ 1 ) } , and the restricted growth curve model (B) μ 2 = { Y , X 1 Θ X 2 | A 1 Θ = B 1 , Θ A 2 = B 2 , σ 2 ( Σ 2 ⊗ Σ 1 ) } , respectively. [ABSTRACT FROM AUTHOR]

In order to tackle parameter estimation of photocounting distributions, polykays of acting intensities are proposed as a new tool for computing photon statistics. As unbiased estimators of cumulants, polykays are computationally feasible thanks to a symbolic method recently developed in dealing with sequences of moments. This method includes the so-called method of moments for random matrices and results to be particularly suited to deal with convolutions or random summations of random vectors. The overall photocounting effect on a deterministic number of pixels is introduced. A random number of pixels is also considered. The role played by spectral statistics of random matrices is highlighted in approximating the overall photocounting distribution when acting intensities are modeled by a non-central Wishart random matrix. Generalized complete Bell polynomials are used in order to compute joint moments and joint cumulants of multivariate photocounters. Multivariate polykays can be successfully employed in order to approximate the multivariate Poisson–Mandel transform. Open problems are addressed at the end of the paper. [ABSTRACT FROM AUTHOR]

The additive Cox model has been considered by many authors. However, the existing methods are either inefficient or their asymptotical properties are not well developed. In this article, we propose a global partial likelihood method to estimate the additive Cox model. We show that the proposed estimator is consistent and asymptotically normal. We also show that the linear functions of the estimated nonparametric components achieve semiparametric efficiency bound. Simulation studies show that our proposed estimator has much less mean squared error than the existing methods. Finally, we apply the proposed approach to the “nursing home” data set (Morris et al. 1994). [ABSTRACT FROM AUTHOR]

We characterize the sets of offspring laws on which the Lotka–Nagaev estimator for the mean of a supercritical Galton–Watson process is qualitatively robust. These are exactly the locally uniformly integrating sets of offspring laws, which may be quite large. If the corresponding global property is assumed instead, we obtain uniform robustness as well. We illustrate both results with a number of concrete examples. As a by-product of the proof we obtain that the Lotka–Nagaev estimator is [locally] uniformly weakly consistent on the respective sets of offspring laws, conditionally on non-extinction. [ABSTRACT FROM AUTHOR]