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Weak convergence and Glivenko-Cantelli results for empirical processes of u-statistic structure

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  • Schneemeier, Wilhelm

Abstract

Empirical processes of U-statistic structure indexed by Vapnik-Chervonenkis classes of sets are studied for independent, but not necessarily identically distributed observations. Glivenko-Cantelli and weak convergence results are obtained by using a representation of these processes as an average of certain empirical processes. This generalizes a theorem of Helmers, Janssen and Serfling (1985) and includes the corresponding results for the empirical process.

Suggested Citation

  • Schneemeier, Wilhelm, 1989. "Weak convergence and Glivenko-Cantelli results for empirical processes of u-statistic structure," Stochastic Processes and their Applications, Elsevier, vol. 33(2), pages 325-334, December.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:2:p:325-334
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    Cited by:

    1. Baringhaus, Ludwig & Gaigall, Daniel, 2015. "On an independence test approach to the goodness-of-fit problem," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 193-208.
    2. Neumeyer, Natalie, 2004. "A central limit theorem for two-sample U-processes," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 73-85, March.

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