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June 1996 The Bahadur-Kiefer representation for U-quantiles
Miguel A. Arcones
Ann. Statist. 24(3): 1400-1422 (June 1996). DOI: 10.1214/aos/1032526976


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.


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Miguel A. Arcones. "The Bahadur-Kiefer representation for U-quantiles." Ann. Statist. 24 (3) 1400 - 1422, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0862.62044
MathSciNet: MR1401857
Digital Object Identifier: 10.1214/aos/1032526976

Primary: 62E20
Secondary: 60F05 , 60F15

Keywords: $U$-statistics , Bahadur-Kiefer epresentations , empirical rocesses , quantiles

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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