Improved estimation of the MSEs and the MSE matrices for shrinkage estimators of multivariate normal means and their applications
نویسنده
چکیده
In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased estimator(UMVUE) under a quadratic loss criterion. A similar improvement is also obtained for the estimators of the MSE matrices for shrinkage estimators. We also apply the proposed estimators of the MSE matrix to form confidence sets centered at shrinkage estimators and show their usefulness through numerical experiments.
منابع مشابه
Shrinkage Preliminary Test Estimation under a Precautionary Loss Function with Applications on Records and Censored Ddata
Shrinkage preliminary test estimation in exponential distribution under a precautionary loss function is considered. The minimum risk-unbiased estimator is derived and some shrinkage preliminary test estimators are proposed. We apply our results on censored data and records. The relative efficiencies of proposed estimators with respect to the minimum ‎risk-unbiased‎&...
متن کاملPositive-Shrinkage and Pretest Estimation in Multiple Regression: A Monte Carlo Study with Applications
Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is a priori known or suspected that a subset of the covariates do not significantly contribute to the overall fit of the model, a restricted model that excludes these covariates, may be sufficient. If, on the other hand, the subset provides useful information, shrinkage meth...
متن کاملOn Mathematical Characteristics of some Improved Estimators of the Mean and Variance Components in Elliptically Contoured Models
In this paper we treat a general form of location model. It is typically assumed that the error term is distributed according to the law belonging to the class of elliptically contoured distribution. Some sorts of shrinkage estimators of location and scale parameters are proposed and their exact bias and MSE expressions are derived. The performance of the estimators under study are compl...
متن کاملTwo-step Smoothing Estimation of the Time-variant Parameter with Application to Temperature Data
‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time...
متن کاملClassic and Bayes Shrinkage Estimation in Rayleigh Distribution Using a Point Guess Based on Censored Data
Introduction In classical methods of statistics, the parameter of interest is estimated based on a random sample using natural estimators such as maximum likelihood or unbiased estimators (sample information). In practice, the researcher has a prior information about the parameter in the form of a point guess value. Information in the guess value is called as nonsample information. Thomp...
متن کامل