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1995•The Annals of StatisticsOpen access

The Asymptotic Accuracy of the Bootstrap of $U$-Quantiles

Miguel A. Arcones

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Quantile, Mathematics, Variance (accounting), Statistics, Order statistic, Econometrics, Business, Accounting

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