Comparison of Some Estimators under the Pitman’s Closeness Criterion in Linear Regression Model

Abstract

Batah et al. (2009) combined the unbiased ridge estimator and principal components regression estimator and introduced the modified $r\text{-}k$ class estimator. They also showed that the modified $r\text{-}k$ class estimator is superior to the ordinary least squares estimator and principal components regression estimator in the mean squared error matrix. In this paper, firstly, we will give a new method to obtain the modified $r\text{-}k$ class estimator; secondly, we will discuss its properties in some detail, comparing the modified $r\text{-}k$ class estimator to the ordinary least squares estimator and principal components regression estimator under the Pitman closeness criterion. A numerical example and a simulation study are given to illustrate our findings.