Cramér-von Mises statistics based on the sample quantile function and estimated parameters

DOI10.1016/0047-259X(86)90061-8zbMath0583.62015MaRDI QIDQ1069225

David M. Mason, Vincent N. La Riccia

Publication date: 1986

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

order statisticsGaussian processcomposite null hypothesisasymptotic null distribution of Cramér-von Mises type statisticsestimated weighted empirical quantile process

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17) Asymptotic properties of parametric tests (62F05)

Related Items (5)

A change detection procedure for an ergodic diffusion process ⋮ Asymptotics for \(L_2\) functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances ⋮ Detection of non-Gaussianity ⋮ Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests. (With comments) ⋮ Goodness-of-fit analysis for multivariate normality based on generalized quantiles.

Cites Work

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• Asymptotic results for goodness-of-fit statistics with unknown parameters
• Asymptotic distributions for quadratic forms with applications to tests of fit
• Weak convergence of the sample distribution function when parameters are estimated
• Approximation Theorems of Mathematical Statistics
• Nonparametric Statistical Data Modeling
• An analysis of variance test for normality (complete samples)

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