On self-normalized sums and student's statistic

Novak, Serguei ORCID: https://orcid.org/0000-0001-7929-7641 (2005) On self-normalized sums and student's statistic. Theory of Probability and Its Applications, 49 (2) . pp. 336-344. ISSN 0040-585X [Article] (doi:10.1137/S0040585X97981081)

Abstract

We evaluate the accuracy of normal approximation for the distributions of some nonlinear functionals of sums of random vectors. A Berry--Esseen type inequality {\em with explicit constants} for the distribution of Student's statistic is established as a consequence of the main result.

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