Improvement of ridge estimator when stochastic restrictions are available in the linear regression model

Abstract

In this paper we propose another ridge type estimator, namely Stochastic Restricted Ordinary Ridge Estimator (SRORE) in the multiple linear regression model when the stochastic restrictions are available in addition to the sample information and when the explanatory variables are multicollinear. Necessary and sufficient conditions for the superiority of the Stochastic Restricted Ordinary Ridge Estimator over the Mixed Estimator (ME), Ridge Estimator (RE) and Stochastic Mixed Ridge Estimator (SMRE) are obtained by using the Mean Square Error Matrix (MSEM) criterion. Finally the theoretical findings of the proposed estimator are illustrated by using a numerical example and a Monte Carlo simulation.