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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.

62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
60F17 Functional limit theorems; invariance principles
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