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

Kenneth S. Alexander and Michel Talagrand

Journal of Multivariate Analysis, 1989, vol. 30, issue 1, 155-166

Abstract: 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.

Keywords: empirical; process; law; of; the; iterated; logarithm; Vapnik-Cervonenkis; class; metric; entropy; weighted; empirical; process (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (4)

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