Bayesian and Non-Bayesian Analysis of the Regression Model with Multivariate Student-tError Terms

Abstract The linear multiple regression model is analyzed assuming the error vector has a multivariate Student-t distribution with zero location vector and scalar dispersion matrix; the multivariate Cauchy and normal distributions are special cases. It is found that the usual least squares coefficient estimate is the maximum likelihood estimate and the mean of the posterior distribution under a diffuse prior distribution. Inferences based on usual t- and F-statistics are shown valid for a range of error distributional assumptions including the multivariate-t assumption. Inferences about the scale parameter of the multivariate-t distribution can be made using an F-distribution rather than the usual χ2 (or inverted χ2) distribution.