DISCO ANALYSIS: A NONPARAMETRIC EXTENSION OF ANALYSIS OF VARIANCE

• 成果类型: Article
• 署名作者: Rizzo, Maria L.; Szekely, Gabor J.
• 署名单位: University System of Ohio; Bowling Green State University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/09-AOAS245
• 发表日期: 2010
• 页码: 1034-1055
• 关键词: multivariate-analysis; distance

摘要

In classical analysis of variance, dispersion is measured by considering squared distances of sample elements from the sample mean. We consider a measure of dispersion for univariate or multivariate response based on all pairwise distances between-sample elements, and derive an analogous distance components (DISCO) decomposition for powers of distance in (0, 2]. The ANOVA F statistic is obtained when the index (exponent) is 2. For each index in (0, 2), this decomposition determines a nonparametric test for the multi-sample hypothesis of equal distributions that is statistically consistent against general alternatives.