The Shapiro-Wilk statistic and its modifications are widely applied in tests for normality. We establish the asymptotic equivalence of a class of statistics based on different choices of normal scores. In particular, we conclude that the Shapiro-Francia, Filliben, Weisberg-Bingham and de Wet-Venter versions of the statistic are asymptotically equivalent. Our results also apply to the Type I and Type II censored data cases.
Publié le : 1987-03-14
Classification:
Correlation tests of normality,
modified Shapiro-Wilk statistics,
Shapiro-Francia statistic,
asymptotic equivalence,
Type I censoring,
Type II censoring,
62F99,
62E20,
62G99
@article{1176350275,
author = {Verrill, Steve and Johnson, Richard A.},
title = {The Asymptotic Equivalence of Some Modified Shapiro-Wilk Statistics-- Complete and Censored Sample Cases},
journal = {Ann. Statist.},
volume = {15},
number = {1},
year = {1987},
pages = { 413-419},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350275}
}
Verrill, Steve; Johnson, Richard A. The Asymptotic Equivalence of Some Modified Shapiro-Wilk Statistics-- Complete and Censored Sample Cases. Ann. Statist., Tome 15 (1987) no. 1, pp. 413-419. http://gdmltest.u-ga.fr/item/1176350275/