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The asymptotic accuracy of the bootstrap of \(U\)-quantiles. (English) Zbl 0845.62035

Summary: The order of the Kolmogorov-Smirnov distance for the bootstrap of \(U\)-quantiles is considered. We observe that the order of the bootstrap of \(U\)-quantiles depends on the order of the local variance of the first term of the Hoeffding decomposition at the \(U\)-quantile. This order can be smaller than the order of the bootstrap of quantiles: \(U\)-quantiles can be smoother than quantiles.

MSC:

62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems
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