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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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Bahadur efficiencies of the Epps--Pulley test for normality
Bruno Ebner, Norbert Henze · 2021-06-26 · via math.ST updates on arXiv.org

The test for normality suggested by Epps and Pulley (1983) is a serious competitor to tests based on the empirical distribution function. In contrast to the latter procedures, it has been generalized to obtain a genuine affine invariant and universally consistent test for normality in any dimension. We obtain approximate Bahadur efficiencies for the test of Epps and Pulley, thus complementing recent results of Milošević et al. (2021). For certain values of a tuning parameter that is inherent in the Epps--Pulley test, this test outperforms each of its competitors considered in Milošević et al. (2021), over the whole range of six close alternatives to normality.

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