The Empirical Bayes Estimations Of Parameters For Multi-classification Model

The issue abuot estimation of linear model has been a hot in statistical research, In this paper, we study empirical Bayes estimations of three-way classification model and Multi-way noninteraction classification model.For the three-way classification model,we get the Bayes estimation of parameter vecter under the assumption of the square loss function and multi-normal prior distirbution.On this basis,we estimate the unknown parameters of the prior distribution using the current samples,then get the empirical estimation of parameter vector through substituting the previous estimates into the Bayes estimation of the unknown parameter vector.Afterwards,we compared the empirical estimation of parameter vector with the least squares estimation of literatue under the standard of mean square error matrix,and proved that the empirical estimation of parameter vector for three-way classification model is superior to the least squares estimation under certain conditions and the standard of mean square error matrix.For the multi-classification model,we obtained the empirical Bayes estimation of parameter vetor using the similar method of the three-way classification model,also found a condition that the empirical estimation of parameter vetor for multi-classification is superior to the the least squares estimation under the standard of mean square error matrix.