Institute of Mathematical Statistics Lecture Notes - Monograph Series

Revisiting two strong approximation results of Dudley and Philipp

Philippe Berthet and David M. Mason

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Abstract

We demonstrate the strength of a coupling derived from a Gaussian approximation of Zaitsev (1987a) by revisiting two strong approximation results for the empirical process of Dudley and Philipp (1983), and using the coupling to derive extended and refined versions of them.

Chapter information

Source
Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn, eds., High Dimensional Probability: Proceedings of the Fourth International Conference (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 155-172

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196284110

Digital Object Identifier
doi:10.1214/074921706000000824

Mathematical Reviews number (MathSciNet)
MR2387767

Zentralblatt MATH identifier
1122.60031

Subjects
Primary: 62E17: Approximations to distributions (nonasymptotic) 62E20: Asymptotic distribution theory
Secondary: 60F15: Strong theorems

Keywords
Gaussian approximation coupling strong approximation

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Berthet, Philippe; Mason, David M. Revisiting two strong approximation results of Dudley and Philipp. High Dimensional Probability, 155--172, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000824. https://projecteuclid.org/euclid.lnms/1196284110


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