Two-sample Kolmogorov-Smirnov-type tests revisited: old and new tests in terms of local levels
type: Item
instance of: scholarly article
title: Two-sample Kolmogorov-Smirnov-type tests revisited: old and new tests in terms of local levels
zbMATH Open document ID: 1416.62246
DOI: 10.1214/17-AOS1647
author: Veronika Gontscharuk
author: Helmut Finner
published in: The Annals of Statistics
publication date: 2018-10-30T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aos/1536307241
review text: To compare the distribution functions of two independent samples of independent observations, the two-sample Kolmogorov Smirnov test, comparing the distance of the empirical distribution function, is useful. Rewriting the test as an union-intersection test, the authors study the local level of the weighted Kolmogorov-Smirnov test, both for finite samples and asymptotically. The authors propose a two-sample test with approximately equal local levels. It is based on the minimum \(p\)-value principle. The authors also study the finite sample properties of this test. They compare the power to the power of the classical Kolmogorov-Smirnov test and the weighted Kolmogorov-Smirnov test. For normal random variables and the alternative of a change in variance, the new test has a good performance. Finally, a combination of the new test and the Kolmogorov-Smirnov test is proposed.
reviewed by: Martin Wendler
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 6968607
zbMATH Keywords: Kolmogorov-Smirnov test
zbMATH Keywords: two-sample test
zbMATH Keywords: local level
MaRDI profile type: Publication
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OpenAlex ID: W2891101911
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description: scientific article; zbMATH DE number 6968607