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

Arcones, Miguel A.

Ann. Stat. 23, No. 5, 1802-1822 (1995).

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

Keywords:

Edgeworth expansion; empirical processes; Kolmogorov-Smirnov distance; bootstrap of \(U\)-quantiles; Hoeffding decomposition