The Annals of Statistics

The Bahadur-Kiefer representation for U-quantiles

Miguel A. Arcones

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Abstract

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

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

Dates
First available in Project Euclid: 20 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032526976

Digital Object Identifier
doi:10.1214/aos/1032526976

Mathematical Reviews number (MathSciNet)
MR1401857

Zentralblatt MATH identifier
0862.62044

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

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

Citation

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


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  • AUSTIN, TEXAS 78712-1082 E-MAIL: arcones@math.utexas.edu