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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximation for bootstrapped
empirical processes


Authors: Miklós Csörgo, Lajos Horváth and Piotr Kokoszka
Journal: Proc. Amer. Math. Soc. 128 (2000), 2457-2464
MSC (1991): Primary 62G30; Secondary 62G07.
Published electronically: November 29, 1999
MathSciNet review: 1676287
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain an approximation for the bootstrapped empirical process with the rate of the Komlós, Major and Tusnády approximation for empirical processes. The proof of the new approximation is based on the Poisson approximation for the uniform empirical distribution function and the Gaussian approximation for randomly stopped sums.


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Additional Information

Miklós Csörgo
Affiliation: Department of Mathematics and Statistics, Carleton University, Ottawa Ontario, Canada K1S 5B6

Lajos Horváth
Affiliation: Department of Mathematics, University of Utah, 155 South 1440 East, Salt Lake City, Utah 84112-0090
Email: horvath@math-utah.edu

Piotr Kokoszka
Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05409-X
PII: S 0002-9939(99)05409-X
Keywords: Bootstrap, empirical process, Poisson process, Brownian bridge, approximations
Received by editor(s): September 16, 1998
Published electronically: November 29, 1999
Additional Notes: The first author’s research was supported by an NSERC Canada grant
The second author’s research was supported by NATO grant CRG 960 503
Dedicated: In memory of Béla Szőkefalvi–Nagy
Communicated by: Wei Y. Loh
Article copyright: © Copyright 2000 American Mathematical Society