Asymptotics for multivariate t-statistic for random vectors in the generalized domain of attraction of the multivariate normal law

Abstract

We define the appropriate analogue of Student's t-statistic for multivariate data, and prove that it is asymptotically normal for random vectors in the Generalized Domain of Attraction of the Normal Law. This extends an earlier result where asymptotic normality was proved under the stronger hypothesis of Domain of Attraction.