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Performances of the Positive-Rule Stein-Type Ridge Estimator in a Linear Regression Model with Spherically Symmetric Error Distributions
Authors:Jianwen Xu  Hu Yang
Institution:1. Department of Statistics and Actuarial Science , Chongqing University , Chongqing , China xjw@cqu.edu.cn;3. Department of Statistics and Actuarial Science , Chongqing University , Chongqing , China
Abstract:In this article, the positive-rule Stein-type ridge estimator (PSRE) is introduced for the parameters in a multiple linear regression model with spherically symmetric error distributions when it is suspected that the parameter vector may be restricted to a linear manifold. The bias and quadratic risk functions of the PSRE are derived and compared with some related competing estimators in literatures. Particularly, some sufficient conditions are derived for superiority of the PSRE over the ordinary ridge estimator, the restricted ridge estimator and the preliminary test ridge estimator, respectively. Furthermore, some graphical results are provided to illustrate some of the theoretical results.
Keywords:Multivariate Student-t distribution  Preliminary test  Quadratic risk  Ridge estimator  Stein-type estimator
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