\(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters (Q1336984)
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scientific article; zbMATH DE number 672058
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters |
scientific article; zbMATH DE number 672058 |
Statements
\(U\)-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of \(U\)-statistics with estimated parameters (English)
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8 November 1994
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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. \textit{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.
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empirical processes
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U-processes
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VC classes of functions
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Vapnik- Cervonenkis classes
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U-statistics with estimated parameters
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trimming of U-statistics
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exponential inequalities
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law of the iterated logarithm
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bootstrap central limit theorem
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