Estimators And Properties For Regression Coefficients In Multivariate Linear Model

In this article, we discuss three kinds of estimators of regression coefficients under three conditions. Firstly, we present an optimal Bayes estimator (BE) of the multivariate linear regression model under misspeeification. This estimator is compared with the ordinary least squares estimator (LSE) in terms of the loss matrix criterion. Some results on admissibility and prediction are also derived. Secondly, we obtain a mixed regression estimator of the multivariate linear regression model under an additional condition. And under the matrix mean square error criterion and Pitman Closeness (PC) criterion, we achieve that this estimator is better than the least square estimator (LSE). Lastly, under misspecified prior assumption the Bayes estimator (BE) of regression coefficients are obtained, based on the loss matrix criterion and posterior Pitman closeness (PPC) criterion, it is compared with the least square estimator (LSE).