Empirical Bayes Estimators Of Parameters For General Partitioned Linear Models

Under the condition of the normal prior distribution and square loss function, the artical expounds the Bayes estimators and empirical Bayes estimators are constructed for the estimable functions of parameters in general partitioned linear models.The artical discusses the Bayes estimators and empirical Bayes estimators are which con-structed for the estimable functions of parameters in three-way partitioned linear models. Under the condition of the normal prior distribution and square loss function, the covariance matrix of the error vectors and prior distribution have unknown parameters. The Bayes estimators of three-way partitioned linear models are constructed. With estimators of unknown parameters in place of unknown parameters of the Bayes estimators, it acquires empirical Bayes estimators for the estimable functions of parameters in three-way partitioned linear models. The superiorities that are investigated of the empirical Bayes estimators for three-way partitioned linear models over ordinary least-squares estimators under mean square error matrix criterion.Finally, the three-way partitioned linear models are extended to general partitioned linear models. The Bayes estimators and empirical Bayes estimators are constructed for the estimable functions of parameters in general partitioned linear models. The superiorities of the empirical Bayes estimators for general partitioned linear models over ordinary least-squares estimators are researched under mean square error matrix criterion.