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May 2017 Two-sample smooth tests for the equality of distributions
Wen-Xin Zhou, Chao Zheng, Zhen Zhang
Bernoulli 23(2): 951-989 (May 2017). DOI: 10.3150/15-BEJ766


This paper considers the problem of testing the equality of two unspecified distributions. The classical omnibus tests such as the Kolmogorov–Smirnov and Cramér–von Mises are known to suffer from low power against essentially all but location-scale alternatives. We propose a new two-sample test that modifies the Neyman’s smooth test and extend it to the multivariate case based on the idea of projection pursue. The asymptotic null property of the test and its power against local alternatives are studied. The multiplier bootstrap method is employed to compute the critical value of the multivariate test. We establish validity of the bootstrap approximation in the case where the dimension is allowed to grow with the sample size. Numerical studies show that the new testing procedures perform well even for small sample sizes and are powerful in detecting local features or high-frequency components.


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Wen-Xin Zhou. Chao Zheng. Zhen Zhang. "Two-sample smooth tests for the equality of distributions." Bernoulli 23 (2) 951 - 989, May 2017.


Received: 1 January 2015; Revised: 1 September 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 1380.62202
MathSciNet: MR3606756
Digital Object Identifier: 10.3150/15-BEJ766

Keywords: Goodness-of-fit , high-frequency alternations , multiplier bootstrap , Neyman’s smooth test , two-sample problem

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability


Vol.23 • No. 2 • May 2017
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