Open Access
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


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.


Download Citation

Kenneth S. Alexander. "The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes." Ann. Probab. 15 (1) 178 - 203, January, 1987.


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

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

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

Vol.15 • No. 1 • January, 1987
Back to Top