We introduce a new Brownian bridge approximation to weighted empirical and quantile processes with rates in probability. This approximation leads to a number of general invariance theorems for empirical and quantile processes indexed by functions. Improved versions of the Chibisov-O'Reilly theorems, the Eicker-Jaeschke theorems for standardized empirical and quantile processes, the normal convergence criterion, and various other old and new asymptotic results on empirical and quantile processes are presented as consequences of our general theorems. In the process, we provide a new characterization of Erdos-Feller-Kolmogorov-Petrovski upper-class functions for the Brownian motion in an improved form.
Publié le : 1986-01-14
Classification:
Weighted empirical and quantile processes,
Brownian bridge approximations,
weak invariance principles indexed by functions,
60F99,
60F17,
60J65,
60F05,
60F20,
62G30
@article{1176992617,
author = {Csorgo, Miklos and Csorgo, Sandor and Horvath, Lajos and Mason, David M.},
title = {Weighted Empirical and Quantile Processes},
journal = {Ann. Probab.},
volume = {14},
number = {4},
year = {1986},
pages = { 31-85},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992617}
}
Csorgo, Miklos; Csorgo, Sandor; Horvath, Lajos; Mason, David M. Weighted Empirical and Quantile Processes. Ann. Probab., Tome 14 (1986) no. 4, pp. 31-85. http://gdmltest.u-ga.fr/item/1176992617/