The Bahadur-Kiefer representation for U-quantiles
Arcones, Miguel A.
Ann. Statist., Tome 24 (1996) no. 6, p. 1400-1422 / Harvested from Project Euclid
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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.
Publié le : 1996-06-14
Classification:  Quantiles,  Bahadur-Kiefer epresentations,  $U$-statistics,  empirical rocesses,  62E20,  60F05,  60F15 
@article{1032526976,
     author = {Arcones, Miguel A.},
     title = {The Bahadur-Kiefer representation for U-quantiles},
     journal = {Ann. Statist.},
     volume = {24},
     number = {6},
     year = {1996},
     pages = { 1400-1422},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1032526976}
}

Arcones, Miguel A. The Bahadur-Kiefer representation for U-quantiles. Ann. Statist., Tome 24 (1996) no. 6, pp.  1400-1422. http://gdmltest.u-ga.fr/item/1032526976/