Comparison of estimators of means based on p-samples from multivariate student-t population

Different strategies for the estimation of the mean for samples from p multivariate Student-t populations in presence of uncertain prior information on the value of the mean in the form of a null hypothesis is investigated. Based on the likelihood function and the uncertain prior information, four different estimators, namely, the unrestricted, restricted, pre-test and shrinkage estimators of the location parameter for a location-scale model are defined. The expressions for the bias, mean square error and risk under quadratic loss function are obtained for each of the estimators. Comparison of the performances of the estimators are made with respect to the mean square error, relative efficiency and quadratic risk under the null as we as the alternative hypotheses. Conclusions regarding the relative performance, dominance picture and inadmissibility of the estimators are also provided.