The Predictive Distributions of the Future Response and Regressor Matrices Under the Multivariate Elliptically Contoured Error Distributions

Abstract

The predictive distributions of the future response and regression matrices under the multivariate elliptically contoured error distributions are considered in this paper. The predictive distributions obtained as matric t which are identical to those obtained under matric normal or matric- t distribution. This gives inference robustness with respect to departures from the reference case of independent sampling from the matric normal or dependent but uncorrelated sampling from matric-t distributions. Some properties of matric t and its successful applications in the field of spatial prediction are addressed. It appears that the matric t distribution has remarkable contribution in various field of statistic.