A Stochastic Restricted Two-Parameter Estimator in Linear Regression Model

Özkale and Kaciranlar (2007 Özakle , M. R. , Kaciranlar , S. ( 2007 ). The restricted and unrestricted two-parameter estimators . Commun. Statist. Theor. Meth. 36 : 2707 – 2725 . Google Scholar]) proposed a two-parameter estimator (TPE) for the unknown parameter vector in linear regression when exact restrictions are assumed to hold. In this article, under the assumption that the errors are not independent and identically distributed, we introduce a new estimator by combining the ideas underlying the mixed estimator (ME) and the two-parameter estimator when stochastic linear restrictions are assumed to hold. The new estimator is called the stochastic restricted two-parameter estimator (SRTPE) and necessary and sufficient conditions for the superiority of the SRTPE over the ME and TPE are derived by the mean squared error matrix (MSEM) criterion. Furthermore, selection of the biasing parameters is discussed and a numerical example is given to illustrate some of the theoretical results.