Approximate Bayesian estimator for the parameter vector in linear models with multivariate t distribution errors

This article constructs an approximate Bayes estimator for the parameter vector consisted of regression coefficients and variance parameter in the linear model in which the error terms follow multivariate t distribution. Its superiorities over the classical estimators are strictly proved in terms of the mean squared error matrix (MSEM) criterion. Compared with the Bayes estimator computed via the MCMC method, the proposed Bayes estimator is simple and easy to interpret and compute, which only requires relatively little prior designation. The numerical computations further verify that the approximate Bayes estimator performs well. Also, the proposed procedure can be easily extended to other multivariate distribution cases.