Open Access
February, 1984 Weak Convergence of the Weighted Empirical Quantile Process in $L^2(0, 1)$
David M. Mason
Ann. Probab. 12(1): 243-255 (February, 1984). DOI: 10.1214/aop/1176993387


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.


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David M. Mason. "Weak Convergence of the Weighted Empirical Quantile Process in $L^2(0, 1)$." Ann. Probab. 12 (1) 243 - 255, February, 1984.


Published: February, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0543.60010
MathSciNet: MR723743
Digital Object Identifier: 10.1214/aop/1176993387

Primary: 60B10
Secondary: 60F05

Keywords: moment bounds , order statistics , weak convergence , Weighted empirical quantile processes

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 1 • February, 1984
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