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December 2012 On the uniform asymptotic validity of subsampling and the bootstrap
Joseph P. Romano, Azeem M. Shaikh
Ann. Statist. 40(6): 2798-2822 (December 2012). DOI: 10.1214/12-AOS1051

Abstract

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These results are then applied (i) to construct confidence regions that behave well uniformly over $\mathbf{P}$ in the sense that the coverage probability tends to at least the nominal level uniformly over $\mathbf{P}$ and (ii) to construct tests that behave well uniformly over $\mathbf{P}$ in the sense that the size tends to no greater than the nominal level uniformly over $\mathbf{P}$. Without these stronger notions of convergence, the asymptotic approximations to the coverage probability or size may be poor, even in very large samples. Specific applications include the multivariate mean, testing moment inequalities, multiple testing, the empirical process and $U$-statistics.

Citation

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Joseph P. Romano. Azeem M. Shaikh. "On the uniform asymptotic validity of subsampling and the bootstrap." Ann. Statist. 40 (6) 2798 - 2822, December 2012. https://doi.org/10.1214/12-AOS1051

Information

Published: December 2012
First available in Project Euclid: 8 February 2013

zbMATH: 1373.62185
MathSciNet: MR3097960
Digital Object Identifier: 10.1214/12-AOS1051

Subjects:
Primary: 62G09, 62G10

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 6 • December 2012
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