The Annals of Probability

Weak Convergence of the Weighted Empirical Quantile Process in $L^2(0, 1)$

David M. Mason

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Probab., Volume 12, Number 1 (1984), 243-255.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993387

Digital Object Identifier
doi:10.1214/aop/1176993387

Mathematical Reviews number (MathSciNet)
MR723743

Zentralblatt MATH identifier
0543.60010

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60F05: Central limit and other weak theorems

Keywords
Weighted empirical quantile processes weak convergence order statistics moment bounds

Citation

Mason, David M. Weak Convergence of the Weighted Empirical Quantile Process in $L^2(0, 1)$. Ann. Probab. 12 (1984), no. 1, 243--255. doi:10.1214/aop/1176993387. https://projecteuclid.org/euclid.aop/1176993387


Export citation