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

Author

Listed:
  • Steffen Betsch

    (Karlsruhe Institute of Technology)

  • Bruno Ebner

    (Karlsruhe Institute of Technology)

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.

Suggested Citation

  • Steffen Betsch & Bruno Ebner, 2020. "Testing normality via a distributional fixed point property in the Stein characterization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 105-138, March.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:1:d:10.1007_s11749-019-00630-0
    DOI: 10.1007/s11749-019-00630-0
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    References listed on IDEAS

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    5. L. Baringhaus & B. Ebner & N. Henze, 2017. "The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 969-995, October.
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    11. J. S. Allison & L. Santana & N. Smit & I. J. H. Visagie, 2017. "An ‘apples to apples’ comparison of various tests for exponentiality," Computational Statistics, Springer, vol. 32(4), pages 1241-1283, December.
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    Cited by:

    1. Ley, Christophe, 2023. "When the score function is the identity function - A tale of characterizations of the normal distribution," Econometrics and Statistics, Elsevier, vol. 26(C), pages 153-160.
    2. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "Testing multivariate normality by zeros of the harmonic oscillator in characteristic function spaces," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 456-501, June.
    3. L. Ndwandwe & J. S. Allison & L. Santana & I. J. H. Visagie, 2023. "Testing for the Pareto type I distribution: a comparative study," METRON, Springer;Sapienza Università di Roma, vol. 81(2), pages 215-256, August.
    4. Bruno Ebner & Norbert Henze, 2023. "On the eigenvalues associated with the limit null distribution of the Epps-Pulley test of normality," Statistical Papers, Springer, vol. 64(3), pages 739-752, June.
    5. Philip Dörr & Bruno Ebner & Norbert Henze, 2021. "A new test of multivariate normality by a double estimation in a characterizing PDE," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 401-427, April.

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