Tightness of the Student $t$-Statistic

Philip S. Griffin (Syracuse University)

Abstract


Let $X, X_1, X_2, \dots $ be a sequence of nondegenerate, independent and identically distributed random variables and set $S_n=X_1+\dots +X_n$,  $V_n^2=X_1^2+\dots +X_n^2$. We answer a question of Gotze, Gine and Mason by providing a simple necessary and sufficient condition for tightness of $S_n/V_n$.

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Pages: 181-190

Publication Date: September 27, 2002

DOI: 10.1214/ECP.v7-1059

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