The Annals of Probability

Bootstrapping the Student t-Statistic

David M. Mason and Qi-Man. Shao

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Abstract

Let $X_1\ldots,X_n, n \geq 1$, be independent, identically distributed random variables and consider the Student $t$-statistic $T_n$ based upon these random variables. Giné, Götze and Mason (1997) proved that $T_n$ converges in distribution to a standard normal random variable if and only if $X$ is in the domain of attraction of a normal random variable and$EX = 0$. We shall show that roughly the same holds true for the bootstrapped Student $t$- statistic $T_n^*$. In the process we shall disclose all the possible subsequential limiting laws of $T_^*n$. The proofs introduce a number of amusing tricks that may be of independent interest.

Article information

Source
Ann. Probab., Volume 29, Number 4 (2001), 1435-1450.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1015345757

Digital Object Identifier
doi:10.1214/aop/1015345757

Mathematical Reviews number (MathSciNet)
MR1880227

Zentralblatt MATH identifier
1010.62026

Subjects
Primary: 62E20: Asymptotic distribution theory 62F12: Asymptotic properties of estimators 60F05: Central limit and other weak theorems

Keywords
Bootstrap Student $t$-statistic order statistics

Citation

Mason, David M.; Shao, Qi-Man. Bootstrapping the Student t -Statistic. Ann. Probab. 29 (2001), no. 4, 1435--1450. doi:10.1214/aop/1015345757. https://projecteuclid.org/euclid.aop/1015345757


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