## 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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