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January, 1986 Weighted Empirical and Quantile Processes
Miklos Csorgo, Sandor Csorgo, Lajos Horvath, David M. Mason
Ann. Probab. 14(1): 31-85 (January, 1986). DOI: 10.1214/aop/1176992617


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.


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Miklos Csorgo. Sandor Csorgo. Lajos Horvath. David M. Mason. "Weighted Empirical and Quantile Processes." Ann. Probab. 14 (1) 31 - 85, January, 1986.


Published: January, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0589.60029
MathSciNet: MR815960
Digital Object Identifier: 10.1214/aop/1176992617

Primary: 60F99
Secondary: 60F05 , 60F17 , 60F20 , 60J65 , 62G30

Keywords: Brownian bridge approximations , weak invariance principles indexed by functions , Weighted empirical and quantile processes

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 1 • January, 1986
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