New difference-based estimator of parameters in semiparametric regression models

The paper introduces a new difference-based Liu estimator β?_Ldiff=([Xtilde]′[Xtilde]+I)^?1([Xtilde]′[ytilde]+η β?_diff) of the regression parameters β in the semiparametric regression model, y=Xβ+f+?. Difference-based estimator, β?_diff=([Xtilde]′[Xtilde])^?1[Xtilde]′[ytilde] and difference-based Liu estimator are analysed and compared with respect to mean-squared error (mse) criterion. Finally, the performance of the new estimator is evaluated for a real data set. Monte Carlo simulation is given to show the improvement in the scalar mse of the estimator.     

An Orthogonality‐Based Estimation of Moments for Linear Mixed Models

Abstract. Estimating higher‐order moments, particularly fourth‐order moments in linear mixed models is an important, but difficult issue. In this article, an orthogonality‐based estimation of moments is proposed. Under only moment conditions, this method can easily be used to estimate the model parameters and moments, particularly those of higher order than the second order, and in the estimators the random effects and errors do not affect each other. The asymptotic normality of all the estimators is provided. Moreover, the method is readily extended to handle non‐linear, semiparametric and non‐linear models. A simulation study is carried out to examine the performance of the new method.     

Robust estimation of AR coefficients under simultaneously influencing outliers and missing values

A family of robust estimators for coefficients of Gaussian AR(p) time series under simultaneously influencing distortions of two types: outliers and missing values, is proposed. The estimators are based on special properties of the Cauchy probability distribution; consistency and the asymptotic normality of these estimators are proven. An approximate solution of the problem of minimization of the asymptotic variance within the proposed family of estimators is found. Performance of the proposed estimators is illustrated for simulated time series and for real data sets.     

Opportunities of the minimum Anderson–Darling estimator as a variant of the maximum likelihood method

We reveal that the minimum Anderson–Darling (MAD) estimator is a variant of the maximum likelihood method. Furthermore, it is shown that the MAD estimator offers excellent opportunities for parameter estimation if there is no explicit formulation for the distribution model. The computation time for the MAD estimator with approximated cumulative distribution function is much shorter than that of the classical maximum likelihood method with approximated probability density function. Additionally, we research the performance of the MAD estimator for the generalized Pareto distribution and demonstrate a further advantage of the MAD estimator with an issue of seismic hazard analysis.     

Wavelet density estimation for negatively associated stratified size-biased sample

This paper provides upper bounds of wavelet estimations on L^p (1≤p<∞) risk for a density function in Besov spaces based on negatively associated stratified size-biased random samples. It turns out that the classical theorem of Donoho, Johnstone, Kerkyacharian and Picard is completely extended to more general cases. More precisely, we consider the model with multiplication noise and allow the sample negatively associated. Our theory is illustrated with a simulation study.     

Testing the equality among distribution functions from independent and right censored samples via Cramér–von Mises criterion

The traditional Cramér–von Mises criterion is used in order to develop a test to compare the equality of the underlying lifetime distributions in the presence of independent censoring times. Its asymptotic distribution is proved and a resampling plan, which is valid for unbalanced data situations, is proposed. Its statistical power is studied and compared with commonly used linear rank tests by Monte Carlo simulations and a real data analysis is also considered. It is observed that the new test is clearly more powerful than the traditional ones when there exists no uniform dominance among involved distributions and in the presence of late differences. Its statistical power is also good in the other considered scenarios.     

Controlling the familywise error rate with plug-in estimator for the proportion of true null hypotheses

Summary.  Estimation of the number or proportion of true null hypotheses in multiple-testing problems has become an interesting area of research. The first important work in this field was performed by Schweder and Spjøtvoll. Among others, they proposed to use plug-in estimates for the proportion of true null hypotheses in multiple-test procedures to improve the power. We investigate the problem of controlling the familywise error rate FWER when such estimators are used as plug-in estimators in single-step or step-down multiple-test procedures. First we investigate the case of independent p -values under the null hypotheses and show that a suitable choice of plug-in estimates leads to control of FWER in single-step procedures. We also investigate the power and study the asymptotic behaviour of the number of false rejections. Although step-down procedures are more difficult to handle we briefly consider a possible solution to this problem. Anyhow, plug-in step-down procedures are not recommended here. For dependent p -values we derive a condition for asymptotic control of FWER and provide some simulations with respect to FWER and power for various models and hypotheses.     

Estimation of Distribution Functions Using Data from Different Environments

Suppose that when a unit operatesin a certain environment, its lifetime has distribution G,and when the unit operates in another environment, its lifetimehas a different distribution, say F. Moreover, supposethe unit is operated for a certain period of time in the firstenvironment and is then transferred to the second environment.Thus we observe a censored lifetime in the first environmentand a failure time of a ``used' unit in the second environment.We propose an EM algorithm approach for obtaining a self-consistentestimator of F. Moreover, suppose using observations from both environments.The case where failure times are subject to right censoring isconsidered as well. We also establish the maximum likelihoodestimator of F. Moreover, suppose when the unit is repairable. Applicationand simulation studies are presented to illustrate the methodsderived.     

Bayesian robustness for multiparameter problems

Bayesian robustness is studied for ε-contamination classes of prior distributions. Nonparametric classes of contsminations such as the class of all unimodal spherically symmetric densities are considered here. Posterior φ-divergence and its curvature are used to measure the sensitivity of priors on the resulting posterior densities. Examples are provided to illustrate our results.     

Convexity-based clustering criteria: theory,algorithms, and applications in statistics

This paper deals with the construction of optimum partitions of for a clustering criterion which is based on a convex function of the class centroids as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszárs -divergence) and for simultaneous classification of the rows and columns of a contingency table.