Efficiency of a stochastic restricted two-parameter estimator in linear regression
A stochastic restricted two-parameter estimator is proposed.The superiority of the new biased estimator over some other estimators is discussed.The selections of the biasing parameters are discussed. Sakallioglu and Kaciranlar (2008) proposed an estimator, two-parameter estimator, as an alternative to the ordinary least squares, the ordinary ridge and the Liu estimators in the presence of multicollinearity. In this paper, we introduce a new class estimator by combining the ideas underlying the mixed estimator and the two-parameter estimator when stochastic linear restrictions are assumed to hold. The necessary and sufficient conditions for the superiority of the new estimator over the two-parameter estimator, modified mixed estimator and stochastic restricted two-parameter estimator Yang and Wu (2012) are derived by the matrix mean square error criterion. Furthermore, selections of the biasing parameters are discussed and two numerical examples and a Monte Carlo simulation are given to evaluate the performance of mentioned estimators in the theoretical results.