The central limit theorem for weighted empirical processes indexed by sets

Kenneth S. Alexander

Journal of Multivariate Analysis, 1987, vol. 22, issue 2, 313-339

Abstract: Sufficient conditions are found for the weak convergence of a weighted empirical process {([nu]n(C)/q(P(C))) 1 [P(C) [succeeds, curly equals] [lambda]n]: C [set membership, variant] }, indexed by a class of sets and weighted by a function q of the size of each set. We find those functions q which allow weak convergence to a sample-continuous Gaussian process, and, given q, determine the fastest rate at which one may allow [lambda]n --> 0.

Keywords: central; limit; theorem; weighted; empirical; process; Vapnik-Cervonenkis; class (search for similar items in EconPapers)
Date: 1987
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