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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
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