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Min-max approach for comparison of univariate normality tests.

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.

SUBMITTER: Islam TU

PROVIDER: S-EPMC8336887 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Min-max approach for comparison of univariate normality tests.

Islam Tanweer Ul TU

PloS one 20210804 8

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 computatio ...[more]

PMID: 34347791

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