Abstract
This paper proposes a new goodness-of-fit test for normality based on the L 2 Wasserstein distance. The authors first construct a probability through the Bootstrap resampling. Although the probability is not distributed uniformly on the interval (0, 1) under the null hypothesis, it is shown that its distribution is free from the unknown parameters, which indicates that such a probability can be taken as the test statistic. It emerges from the simulation study of power that the new test is able to better discriminate between the normal distribution and those distributions with short tails. For such alternatives, it has a substantially better power than existing tests including the Anderson-Darling test and Shapiro-Wilk test, which are two of the best tests for normality. In addition, the sensitivity analysis of tests is also investigated in the presence of moderate perturbation, which shows that the new test is a rather robust test.
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 11201005 and 11071015, the Natural Science Foundation of Anhui Province under Grant Nos. 1308085QA13 and 1208085MA11, and the Key Project of Anhui Education Committee under Grant Nos. KJ2012A135 and 2012SQRL028ZD.
This paper was recommended for publication by Editor ZOU Guohua.
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He, D., Xu, X. & Zhao, J. A new procedure for testing normality based on the L 2 Wasserstein distance. J Syst Sci Complex 26, 572–582 (2013). https://doi.org/10.1007/s11424-013-1221-7
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DOI: https://doi.org/10.1007/s11424-013-1221-7