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\(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters. (English) Zbl 0807.62014
New results on exponential inequalities, on the law of the iterated logarithm and on the bootstrap central limit theorem for \(U\)-processes indexed by so-called \(VC\) classes of functions [cf. R. M. Dudley, Lect. Notes Math. 1097, 1-142 (1984; Zbl 0554.60029)] are derived. These results are then applied to the asymptotics and the bootstrap of \(U\)- statistics with estimated parameters, in particular to the trimming of U- statistics. Earlier results are improved and extended.
Reviewer: L.Paditz (Dresden)

62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
60F15 Strong limit theorems
62G20 Asymptotic properties of nonparametric inference
Full Text: DOI
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