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VOL. 46 | 2004 Stein’s method for the bootstrap

Abstract

This paper gives new proofs for many known results about the convergence in law of the bootstrap distribution to the true distribution of smooth statistics, whether the samples studied come from independent realizations of a random variable or dependent realizations with weak dependence. Moreover it suggests a novel bootstrap procedure and provides a proof that this new bootstrap works under uniform local dependence. The techniques employed are based on Stein’s method for empirical processes as developed by Reinert (1994). A weak law of large numbers for empirical measures via Stein’s method and applications. The last section provides some simulations and applications for which the relevant matlab functions are available from the first author.

Information

Published: 1 January 2004
First available in Project Euclid: 28 November 2007

MathSciNet: MR2118605

Digital Object Identifier: 10.1214/lnms/1196283802

Rights: Copyright © 2004, Institute of Mathematical Statistics

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