Quadratic Structural Bayes Estimator For Parameters In Normal Linear Model

The normal linear model is a very important model in mathematical statistics.Para-meter estimator is a core area in the normal linear model.There are several methods have been put forward and commonly used,such as the least squares estimator,the maximum likelihood estimator and the Bayes estimator.Bayes estimator is usually a nonlinear function of samples,and it is hard to get a explicit expression due to the complex double integral in the calculation.In this paper,we put forward a Bayes estimator based on quadratic form statistics for parameters in the normal linear model.This method combines Bayes theory,the suf-ficient statistics of samples and some knowledge about the quadratic form.It uses the prior information,at the same time avoids the tedious calculation of the posterior expec-tation.Ensuring the accuracy of estimators,we provide a explicit quadratic structural Bayes estimator expression for parameters in the normal linear models.First,based on this method,we obtain the quadratic structural Bayes estimator expression for parameters in the normal linear model using three statistics (?),(?)2 and(?)'X'X(?).Then in terms of the mean square error criterion,we come to the result that the quadratic structural Bayes estimator using three sufficient statistics is superior to the linear Bayes estimator using two statistics (?)' and (?)2,and is also superior to the least squares estimator and the maximum likelihood estimator of parameters.Finally,in the cases of the priors of two parameters are independent or dependent,we select different prior distributions to investigate our conclusion through numerical simulations.We verify that the relative error between the quadratic structural Bayes estimator and Bayes estimator decreases as the sample size gets large and the priors information gets more and more concentrated.