Berthet, Mason: Revisiting two strong approximation results of Dudley and Philipp

Revisiting two strong approximation results of Dudley and Philipp

Philippe Berthet, David M. Mason

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.

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.

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Primary Subjects: 62E17, 62E20

Secondary Subjects: 60F15

Keywords: Gaussian approximation; coupling; strong approximation

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196284110
Digital Object Identifier: doi:10.1214/074921706000000824

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Revisiting two strong approximation results of Dudley and Philipp

Abstract

Institute of Mathematical Statistics Lecture Notes - Monograph Series