We consider the Wasserstein distance between a sample distribution
and the set of normal distributions as a measure of nonnormality. By
considering the standardized version of this distance we obtain a version of
Shapiro–Wilk’s test of normality. The asymptotic behavior of the
statistic is studied using approximations of the quantile process by Brownian
bridges. This method differs from the “ad hoc” method of de Wet
and Venter and permits a similar analysis for testing other location scale
families.
Publié le : 1999-08-14
Classification:
Wasserstein distance,
correlation test,
Shapiro-Wilk,
goodness of fit,
test of normality,
quantile process,
Brownian bridge,
convergence of integrals,
62F05,
62E20,
60F25
@article{1017938923,
author = {del Barrio, Eustasio and Cuesta-Albertos, Juan A. and Matr\'an, Carlos and Rodr\'\i guez-Rodr\'\i guez, Jes{\'u}s M.},
title = {Tests of goodness of fit based on the $L\_2$-Wasserstein
distance},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1230-1239},
language = {en},
url = {http://dml.mathdoc.fr/item/1017938923}
}
del Barrio, Eustasio; Cuesta-Albertos, Juan A.; Matrán, Carlos; Rodríguez-Rodríguez, Jes{\'u}s M. Tests of goodness of fit based on the $L_2$-Wasserstein
distance. Ann. Statist., Tome 27 (1999) no. 4, pp. 1230-1239. http://gdmltest.u-ga.fr/item/1017938923/