Title

A Note On Goodness-Of-Fit Statistics With Asymptotically Normal Distributions

Keywords

Asymptotic normality; Cramér-vonMises statistics; Distribution free; Goodness of fit tests; Testing symmetry; Two-sample problems; Watson test

Abstract

A generalization of the Cramér-vonMises L2 distance is proposed. It gives rise to a class of goodness-of-fit statistics that is difficult to analyze using traditional techniques based on empirical distributions but can easily be modified to yield null and non null limiting normal distributions. The family index may be used to maximize the power of the test for a specific alternative hypothesis. The procedure presented here is shown to work for Watson's modification for circular data and also when testing symmetry about the zero. The problem of testing two-samples is also presented. All procedures presented here are distributions-free and can be used equally for univariate or multivariate data.

Publication Date

1-1-2001

Publication Title

Journal of Nonparametric Statistics

Volume

13

Issue

4

Number of Pages

485-500

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/10485250108832862

Socpus ID

0345856508 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0345856508

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