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

• Steffen Betsch ^[1] ; Bruno Ebner ^[1]
  1. [1] Karlsruhe Institute of Technology

     Karlsruhe Institute of Technology

     Stadtkreis Karlsruhe, Alemania

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 29, Nº. 1, 2020, págs. 105-138
• Idioma: inglés
• DOI: 10.1007/s11749-019-00630-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on 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.