On Standard Normal Convergence of the Multivariate Student $t$-Statistic for Symmetric Random Vectors

摘要

It is proved that if the multivariate Student $t$-statistic based on i.i.d. symmetric random vectors is asymptotically standard normal, then these random vectors are in the generalized domain of attraction of the normal law. Uniform integrability is also considered, even in the absence of symmetry.