Telford, A, Taylor, CC orcid.org/0000-0003-0181-1094, Wood, HM orcid.org/0000-0003-3009-5904 et al. (1 more author) (2020) Properties and approximate p-value calculation of the Cramer test. Journal of Statistical Computation and Simulation, 90 (11). pp. 1965-1981. ISSN 0094-9655
Abstract
Two-sample tests are probably the most commonly used tests in statistics. These tests generally address one aspect of the samples' distribution, such as mean or variance. When the null hypothesis is that two distributions are equal, the Anderson–Darling (AD) test, which is developed from the Cramer–von Mises (CvM) test, is generally employed. Unfortunately, we find that the AD test often fails to identify true differences when the differences are complex: they are not only in terms of mean, variance and/or skewness but also in terms of multi-modality. In such cases, we find that Cramer test, a modification of the CvM test, performs well. However, the adaptation of the Cramer test in routine analysis is hindered by the fact that the mean, variance and skewness of the test statistic are not available, which resulted in the problem of calculating the associated p-value. For this purpose, we propose a new method for obtaining a p-value by approximating the distribution of the test statistic by a generalized Pareto distribution. By approximating the distribution in this way, the calculation of the p-value is much faster than e.g. bootstrap method, especially for large n. We have observed that this approximation enables the Cramer test to have proper control of type-I error. A simulation study indicates that the Cramer test is as powerful as other tests in simple cases and more powerful in more complicated cases.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Informa UK Limited, trading as Taylor & Francis Group. This is an author produced version of an article published in Journal of Statistical Computation and Simulation. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Two-sample tests, cumulative distribution, multi-modality, Cramer test, Anderson–Darling, Cramer–von Mises |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Mar 2022 16:41 |
Last Modified: | 19 Mar 2022 20:37 |
Status: | Published |
Publisher: | Routledge |
Identification Number: | 10.1080/00949655.2020.1754820 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:184852 |