EDF goodness-of-fit tests based on centre-outward ordering

Jun Li

Journal of Nonparametric Statistics, 2018, vol. 30, issue 4, 973-989

Abstract: The Kolmogorov-Smirnov (KS) test, the Cramér-von Mises (CvM) test, and the Anderson-Darling (AD) test are widely used goodness-of-fit tests based on the empirical distribution function (EDF). When defining the EDF in those tests, the data are ordered from the smallest to the largest. This left-to-right ordering partly explains why the three EDF tests are only sensitive to location differences but not to scale differences. Motivated by this observation, we propose three EDF tests based on the centre-outward ordering and they are shown to be more powerful than the KS, CvM and AD tests for detecting scale differences. To detect any arbitrary distributional differences, we further propose to combine our newly developed centre-outward ordering based EDF tests with the original EDF tests. The combined tests are easy to implement and are shown to have good performance detecting a variety of distributional differences. The extension of the results to the two-sample comparison problem is also discussed.

Date: 2018
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DOI: 10.1080/10485252.2018.1508676

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