On the Stein-Type Liu Estimator and Positive-Rule Stein-Type Liu Estimator in Multiple Linear Regression Models

Abstract

In this article, the Stein-type Liu estimator and positive-rule Stein-type Liu estimator are constructed for the parameter vector in a multiple linear model under a multicollinearity situation when it is suspected that the regression coefficients may be restricted to a subspace. Biases and quadratic risks of the proposed estimators are derived and compared to some competitors in literatures, such as the Liu estimator by Liu (1993), the restricted Liu estimator by Kaçıranlar et al. (1999), and the preliminary test Liu estimator by Yang and Xu (2011). Furthermore, some simulation results are provided to illustrate some of the theoretical results.