The Small-sample Properties for the Bayes Estimator of Regression Coefficients under Misspecified Prior Assumption

In this artical, under misspecified prior assumption the Bayes estimator （BE） of regrtession coefficients are obtained, based on the mean square error matrix criterion, it is compared with least square estimator （LSE）. The bounds of the relative efficiencies for the considered estimators are derived. Filially, under the posterior Pitman closeness （PPC） criterion, the superiority of the BE over LSE is discussed.