DISCO analysis: A nonparametric extension of analysis of variance

Details DISCO analysis: A nonparametric extension of analysis of variance DISCO analysis: A nonparametric extension of analysis of variance

2010-11-10

arxiv.org/abs/1011.2288v1

Annals of Applied Statistics 2010, Vol. 4, No. 2, 1034-1055

Statistics

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Published in at http://dx.doi.org/10.1214/09-AOAS245 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

10.1214/09-AOAS245

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.

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