DISCO analysis: A nonparametric extension of analysis of variance

By Maria L. Rizzo, G'abor J. Sz'ekely. 2010

153 citations recorded by the source corpus.

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.

Subfields: Analytical Chemistry, Food Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4eba67eab217405326174b90298748c5f36f5cc1

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In Analytical Chemistry

In Food Science

In Statistics and Probability

Citations in the corpus

Energy statistics: A class of statistics based on distances (2013, methodology): “The power of the DISCO test of the multisample hypothesis H0 : F1 ¼⋯¼ FK is illustrated in the following power comparison.”
ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data (2013, methodology): “In Section 2 we introduce the energy statistic of Székely and Rizzo (2005, 2010), which is the fundamental divergence measure applied for change point analysis.”
A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data (2013, methodology): “For univariate observations with continuous distributions the familiar Kolmogorov–Smirnov test may be applied, and in the general case the approach in Rizzo and Székely (2010) may be applied.”
Energy distance (2016, methodology): “(4) determines a consistent test of the multi-sample hypothesis of equal distributions.(13) In the special case where all Fj are univariate distributions and α = 2, Sn,2 is the ANOVA between sample sum of squared error and the decomposition T2 = S2 + W2 is the ANOVA decomposition.”