Tightness of the student T-statistic

Philip S. Griffin

doi:10.1214/ECP.v7-1059

Tightness of the student T-statistic

Philip S. Griffin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let X, X₁, X₂, … be a sequence of nondegenerate, independent and identically distributed random variables and set S_n = X₁ + ⋯ + X_n, V²_n = X²₁ + ⋯ + X²_n. We answer a question of Götze, Giné and Mason by providing a simple necessary and sufficient condition for tightness of S_n/V_n.

Original language	English (US)
Pages (from-to)	181-190
Number of pages	10
Journal	Electronic Communications in Probability
Volume	7
DOIs	https://doi.org/10.1214/ECP.v7-1059
State	Published - Jan 1 2002

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/ECP.v7-1059

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abstract = "Let X, X1, X2, … be a sequence of nondegenerate, independent and identically distributed random variables and set Sn = X1 + ⋯ + Xn, V2n = X21 + ⋯ + X2n. We answer a question of G{\"o}tze, Gin{\'e} and Mason by providing a simple necessary and sufficient condition for tightness of Sn/Vn.",

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N2 - Let X, X1, X2, … be a sequence of nondegenerate, independent and identically distributed random variables and set Sn = X1 + ⋯ + Xn, V2n = X21 + ⋯ + X2n. We answer a question of Götze, Giné and Mason by providing a simple necessary and sufficient condition for tightness of Sn/Vn.

AB - Let X, X1, X2, … be a sequence of nondegenerate, independent and identically distributed random variables and set Sn = X1 + ⋯ + Xn, V2n = X21 + ⋯ + X2n. We answer a question of Götze, Giné and Mason by providing a simple necessary and sufficient condition for tightness of Sn/Vn.

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JO - Electronic Communications in Probability

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ER -

Tightness of the student T-statistic

Abstract

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