The law of the iterated logarithm for empirical processes on Vapnik-Cervonenkis classes

Necessary and sufficient conditions are established for the bounded and compact laws of the iterated logarithm for empirical processes indexed by classes of functions which have the Vapnik-Cervonenkis property. Results of Ledoux and Talagrand (Ann. Probab. 16 1242-1264, and in press) reduce the problem fromone of almostsure behavior to one of in-probability behavior. The special case of weighted empirical processes indexed by sets is considered.

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Year of publication:	1989
Authors:	Alexander, Kenneth S. ; Talagrand, Michel
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 30.1989, 1, p. 155-166
Publisher:	Elsevier
Keywords:	empirical process law of the iterated logarithm Vapnik-Cervonenkis class metric entropy weighted empirical process

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005199372