Tests of goodness of fit based on the L2-Wasserstein distance

• 成果类型: Article
• 署名作者: Del Barrio, E; Cuesta-Albertos, JA; Matrán, C; Rodríguez-Rodríguez, JM
• 署名单位: Universidad de Valladolid; Universidad de Cantabria
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1230-1239
• 关键词: quantile processes; distributions; normality

摘要

Ne 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 me 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.