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Rates of convergence for U-statistic processes and their bootstrapped versions. (English) Zbl 1005.62046
Summary: $$U$$-statistic processes are often used to detect a possible change in the distributions of the observations. We obtain the exact rate of convergence in some limit theorems for $$U$$-statistics. We discuss the application of the weighted bootstrap to change-point analysis. We show that the bootstrap approximation for $$U$$-statistics is as good as the large sample approximations using Gaussian processes. However, the bootstrap approximation is much better when the limit distributions are extreme values.

##### MSC:
 62G09 Nonparametric statistical resampling methods 62G20 Asymptotic properties of nonparametric inference 60F17 Functional limit theorems; invariance principles
##### Keywords:
change-point; U-statistics; bootstrap; approximations; extreme values
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##### References:
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