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

Evarist Giné (University of Connecticut, USA)
Friedrich Götze (Universitat Bielefeld)

Abstract


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.

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Pages: 162-171

Publication Date: November 17, 2004

DOI: 10.1214/ECP.v9-1120

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