A Research On The Superiority Of Bayes Linear Unbiased Variance Estimator In The Generalized Gauss-Markov Model

Liner model is one of most important statistical models in mathematical statistics,which has many applications in economy, biology, military and other fields. And thestudy of linear model mainly concentrated in parameter estimation. As for the problemof parameters estimation, the least square estimate(LSE) is one of most radical and typicestimate. With the rapid development of the statistics, we know that LSE is not a goodestimate in many conditions. Therefore, in this paper, the Bayes linear unbiasedestimators (Bayes LUE) of parameters and it’s properties are studied in the generalizedGauss-Markov model.Firstly, this paper briefly analyze the basic theory of Bayes statistics and linermodel, including statistical decision, prior distribution and posterior distribution, riskfunction，least square method and Bayes estimation method. Secondly, we obtain theBayes LUE of parameters in the generalized Gauss-Markov model by Bayes estimationmethod. Then we compare the Bayes estimator with generalized least squareestimator(GLSE) under the mean square error matrix criterion and PC criterionconditions. Finally, we obtain the bounds of four relative efficiencies, when the priordistribution is misspecified. At last, we should recognize that Bayes LUE is a betterEstimation method than the GLSE in the generalized Gauss-Markov model.