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August 1999 Tests of goodness of fit based on the $L_2$-Wasserstein distance
Juan A. Cuesta-Albertos, Carlos Matrán, Jes{\'u}s M. Rodríguez-Rodríguez, Eustasio del Barrio
Ann. Statist. 27(4): 1230-1239 (August 1999). DOI: 10.1214/aos/1017938923


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.


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Juan A. Cuesta-Albertos. Carlos Matrán. Jes{\'u}s M. Rodríguez-Rodríguez. Eustasio del Barrio. "Tests of goodness of fit based on the $L_2$-Wasserstein distance." Ann. Statist. 27 (4) 1230 - 1239, August 1999.


Published: August 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0961.62037
MathSciNet: MR1740113
Digital Object Identifier: 10.1214/aos/1017938923

Primary: 62E20 , 62F05
Secondary: 60F25

Keywords: Brownian bridge , convergence of integrals , correlation test , goodness of fit , quantile process , Shapiro-Wilk , test of normality , Wasserstein distance

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • August 1999
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