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January, 1987 The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes
Kenneth S. Alexander
Ann. Probab. 15(1): 178-203 (January, 1987). DOI: 10.1214/aop/1176992263

Abstract

Sufficient conditions, which under weak additional assumptions are also necessary, are found for the central limit theorem for empirical processes indexed by classes of functions which have the Vapnik-Cervonenkis property. This improves an earlier theorem of Pollard (1982a), and leads to necessary and sufficient conditions for the CLT for weighted empirical processes indexed by Vapnik-Cervonenkis classes of sets.

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Kenneth S. Alexander. "The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes." Ann. Probab. 15 (1) 178 - 203, January, 1987. https://doi.org/10.1214/aop/1176992263

Information

Published: January, 1987
First available in Project Euclid: 19 April 2007

zbMATH: 0624.60032
MathSciNet: MR877597
Digital Object Identifier: 10.1214/aop/1176992263

Subjects:
Primary: 60F05
Secondary: 60B12 , 60F17

Keywords: central limit theorem , empirical process , Metric entropy , Vapnik-Cervonenkis class , weighted empirical process

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • January, 1987
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