Limiting behavior of the perturbed empirical distribution functions evaluated at \(U\)-statistics for strongly mixing sequences of random variables (Q1357890)
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scientific article; zbMATH DE number 1023065
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Limiting behavior of the perturbed empirical distribution functions evaluated at \(U\)-statistics for strongly mixing sequences of random variables |
scientific article; zbMATH DE number 1023065 |
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Limiting behavior of the perturbed empirical distribution functions evaluated at \(U\)-statistics for strongly mixing sequences of random variables (English)
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27 July 1997
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Summary: We prove the almost sure representation, a law of the iterated logarithm and an invariance principle for the statistic \(\widehat{F}_n(U_n)\) for a class of strongly mixing sequences of random variables \(\{X_i, i\geq 1\}\). Stationarity is not assumed. Here \(\widehat{F}_n\) is the perturbed empirical distribution function and \(U_n\) is a \(U\)-statistic based on \(X_1,\dots,X_n\).
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almost sure representation
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law of the iterated logarithm
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invariance principle
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strongly mixing sequences of random variables
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perturbed empirical distribution function
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\(U\)-statistic
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