Testing normality via a distributional fixed point property in the Stein characterization

Steffen Betsch () and Bruno Ebner ()
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Steffen Betsch: Karlsruhe Institute of Technology
Bruno Ebner: Karlsruhe Institute of Technology

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2020, vol. 29, issue 1, No 7, 105-138

Abstract: Abstract We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $$L^2$$L2-distances of the empirical zero-bias transformation to the empirical distribution or the normal distribution function. Weak convergence results are derived under the null hypothesis, under contiguous as well as under fixed alternatives. A comparative finite-sample power study shows the competitiveness to classical procedures.

Keywords: Goodness-of-fit test; Normal distribution; Stein’s method; Zero-bias transformation; Primary 62F03; Secondary 62F05; 60E10; 62E10 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s11749-019-00630-0

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