Twenty years have elapsed since the Shapiro-Wilk statistic $W$ for testing the normality of a sample first appeared. In that time a number of statistics that are close relatives of $W$ have been found to have a common (known) asymptotic distribution. It was assumed, therefore, that $W$ must have that asymptotic distribution. We show this to be the case and examine the norming constants that are used with all the statistics. In addition the consistency of the $W$ test is established.
Publié le : 1986-12-14
Classification:
Shapiro-Wilk statistic,
goodness of fit,
normal order scores,
tests of normality,
62F05,
62E20,
62G30
@article{1176350172,
author = {Leslie, J. R. and Stephens, M. A. and Fotopoulos, S.},
title = {Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 1497-1506},
language = {en},
url = {http://dml.mathdoc.fr/item/1176350172}
}
Leslie, J. R.; Stephens, M. A.; Fotopoulos, S. Asymptotic Distribution of the Shapiro-Wilk $W$ for Testing for Normality. Ann. Statist., Tome 14 (1986) no. 2, pp. 1497-1506. http://gdmltest.u-ga.fr/item/1176350172/