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October 2001 Bootstrapping the Student t-Statistic
David M. Mason, Qi-Man. Shao
Ann. Probab. 29(4): 1435-1450 (October 2001). DOI: 10.1214/aop/1015345757


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.


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David M. Mason. Qi-Man. Shao. "Bootstrapping the Student t-Statistic." Ann. Probab. 29 (4) 1435 - 1450, October 2001.


Published: October 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1010.62026
MathSciNet: MR1880227
Digital Object Identifier: 10.1214/aop/1015345757

Primary: 60F05 , 62E20 , 62F12

Keywords: bootstrap , order statistics , Student $t$-statistic

Rights: Copyright © 2001 Institute of Mathematical Statistics

Vol.29 • No. 4 • October 2001
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