The Annals of Statistics

The Bahadur-Kiefer representation for U-quantiles

Miguel A. Arcones

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We consider the distributional and the almost sure pointwise Bahadur-Kiefer representation for U-quantiles. We show that the order of this representation depends on the order of the local variance of the empirical process of U-statistic structure at the U-quantile. Our results indicate that U-quantiles can be smoother than quantiles. U-quantiles can either be as unsmooth as quantiles or can behave as differentiable statistical functionals.

Article information

Ann. Statist., Volume 24, Number 3 (1996), 1400-1422.

First available in Project Euclid: 20 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E20: Asymptotic distribution theory
Secondary: 60F05: Central limit and other weak theorems 60F15: Strong theorems

Quantiles Bahadur-Kiefer epresentations $U$-statistics empirical rocesses


Arcones, Miguel A. The Bahadur-Kiefer representation for U -quantiles. Ann. Statist. 24 (1996), no. 3, 1400--1422. doi:10.1214/aos/1032526976.

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