Cramér-von Mises statistics based on the sample quantile function and estimated parameters
type: Item
instance of: scholarly article
title: Cramér-von Mises statistics based on the sample quantile function and estimated parameters
zbMATH Open document ID: 0583.62015
DOI: 10.1016/0047-259X(86)90061-8
author: David M. Mason
author: Vincent N. La Riccia
published in: Journal of Multivariate Analysis
publication date: 1986-01-01T00:00:00Z
review text: The estimated weighted empirical quantile process is introduced, and under mild regularity conditions is shown to converge weakly in \(L^ 2(0,1)\) to a Gaussian process. This leads to an elementary approach to the derivation of the asymptotic null distribution of Cramér-von Mises type statistics for testing a composite null hypothesis based on the sample quantile function and estimated parameters. Special emphasis is given to the location/scale composite null hypothesis.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62F05
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3934200
zbMATH Keywords: order statistics
zbMATH Keywords: estimated weighted empirical quantile process
zbMATH Keywords: Gaussian process
zbMATH Keywords: asymptotic null distribution of Cramér-von Mises type statistics
zbMATH Keywords: composite null hypothesis
MaRDI profile type: Publication
cites work: Q4404205
cites work: Q5560061
cites work: A differential for L-statistics
cites work: Approximations of the empirical process when parameters are estimated
cites work: Q3326516
cites work: Q3667777
cites work: Q4072649
cites work: Asymptotic distributions for quadratic forms with applications to tests of fit
cites work: Weak convergence of the sample distribution function when parameters are estimated
cites work: Q3324840
cites work: Q4153935
cites work: Asymptotic properties of weighted \(L^ 2\) quantile distance estimators
cites work: Weak convergence of the weighted empirical quantile process in \(L^ 2(0,1)\)
cites work: Q4125569
cites work: Q5533878
cites work: Nonparametric Statistical Data Modeling
cites work: Approximation Theorems of Mathematical Statistics
cites work: An analysis of variance test for normality (complete samples)
cites work: Asymptotic results for goodness-of-fit statistics with unknown parameters
description: scientific article; zbMATH DE number 3934200