Sufficient conditions are developed for various versions of the weighted empirical quantile process to converge weakly in $L^2(0, 1)$ to a weighted Brownian bridge. The results are directly applicable to the derivation of the asymptotic distribution of goodness of fit tests based on the sample quantiles that can be written as a functional defined on $L^2(0, 1)$ continuous in the norm topology. In the process, tight bounds for the moments of transformed uniform order statistics are derived that are likely to have applications elsewhere.
Publié le : 1984-02-14
Classification:
Weighted empirical quantile processes,
weak convergence,
order statistics,
moment bounds,
60B10,
60F05
@article{1176993387,
author = {Mason, David M.},
title = {Weak Convergence of the Weighted Empirical Quantile Process in $L^2(0, 1)$},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 243-255},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993387}
}
Mason, David M. Weak Convergence of the Weighted Empirical Quantile Process in $L^2(0, 1)$. Ann. Probab., Tome 12 (1984) no. 4, pp. 243-255. http://gdmltest.u-ga.fr/item/1176993387/