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

Wilhelm Schneemeier

Stochastic Processes and their Applications, 1989, vol. 33, issue 2, 325-334

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.

Keywords: empirical; process; U-statistic; b-convergence; pseudo-metric; *; Vapnik-Chervonenkis; classes; of; sets (search for similar items in EconPapers)
Date: 1989
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