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Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance

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  • Xiang, Jim X.

Abstract

In this paper we derive a formula for the sample size of a nonparametric test based on weighted L2-Wasserstein distance with a known alternative. As an example we apply the formula to determine the sample size for a hypothesis testing from the Tukey’s contaminated distribution model. The reliability of the sample size formula is evaluated in terms of type I errors and the powers of the test. The Monte Carlo simulation results show that the test based on the weighted L2-Wasserstein distance performs equally well as the Anderson–Darling test and is superior to the Kolmogorov–Smirnov and the Cramer–von Mises tests.

Suggested Citation

  • Xiang, Jim X., 2017. "Sample size determination of a nonparametric test based on weighted L2-Wasserstein distance," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 160-164.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:160-164
    DOI: 10.1016/j.spl.2016.11.023
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    References listed on IDEAS

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    1. T. Wet, 2002. "Goodnes-of-fit tests for location and scale families based on a weighted L 2 -Wasserstein distance measure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 89-107, June.
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