Min-max approach for comparison of univariate normality tests

Tanweer Islam

PLOS ONE, 2021, vol. 16, issue 8, 1-19

Abstract: Comparison of normality tests based on absolute or average powers are bound to give ambiguous results, since these statistics critically depend upon the alternative distribution which cannot be specified. A test which is optimal against a certain type of alternatives may perform poorly against other alternative distributions. Thus, an invariant benchmark is proposed in the recent normality literature by computing Neyman-Pearson tests against each alternative distribution. However, the computational cost of this benchmark is significantly high, therefore, this study proposes an alternative approach for computing the benchmark. The proposed min-max approach reduces the calculation cost in terms of computing and estimating the Neyman-Pearson tests against each alternative distribution. An extensive simulation study is conducted to evaluate the selected normality tests using the proposed methodology. The proposed min-max method produces similar results in comparison with the benchmark based on Neyman-Pearson tests but at a low computational cost.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0255024

DOI: 10.1371/journal.pone.0255024

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