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The central limit theorem for weighted empirical processes indexed by sets

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  • Alexander, Kenneth S.

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.

Suggested Citation

  • Alexander, Kenneth S., 1987. "The central limit theorem for weighted empirical processes indexed by sets," Journal of Multivariate Analysis, Elsevier, vol. 22(2), pages 313-339, August.
    • Handle: RePEc:eee:jmvana:v:22:y:1987:i:2:p:313-339
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    Cited by:

    1. Ziegler, Klaus, 1997. "Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 233-272, August.

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