Necessary Conditions for the Bootstrap of the Mean

Evarist Gine; Joel Zinn

doi:10.1214/aos/1176347134

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Home > Journals > Ann. Statist. > Volume 17 > Issue 2 > Article

June, 1989 Necessary Conditions for the Bootstrap of the Mean

Evarist Gine, Joel Zinn

Ann. Statist. 17(2): 684-691 (June, 1989). DOI: 10.1214/aos/1176347134

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Abstract

It is proved that $EX^2 < \infty$ is necessary for a very mild form of the bootstrap of the mean to work a.s. and that $X$ must be in the domain of attraction of the normal law if a.s. is weakened to "in probability."

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Evarist Gine. Joel Zinn. "Necessary Conditions for the Bootstrap of the Mean." Ann. Statist. 17 (2) 684 - 691, June, 1989. https://doi.org/10.1214/aos/1176347134