## The Annals of Probability

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

David M. Mason

#### 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

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
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