Decomposability of high-dimensional diversity measures: Quasi-U-statistics, martingales and nonstandard asymptotics

Aluísio Pinheiro, Pranab Kumar Sen and Hildete Prisco Pinheiro

Journal of Multivariate Analysis, 2009, vol. 100, issue 8, 1645-1656

Abstract: In analyses of complex diversity, especially that arising in genetics, genomics, ecology and other high-dimensional (and sometimes low-sample-size) data models, typically subgroup decomposability (analogous to ANOVA decomposability) arises. For group divergence of diversity measures in a high-dimension low-sample-size scenario, it is shown that Hamming distance type statistics lead to a general class of quasi-U-statistics having, under the hypothesis of homogeneity, a martingale (array) property, providing a key to the study of general (nonstandard) asymptotics. Neither the stochastic independence nor homogeneity of the marginal probability laws plays a basic role. A genomic MANOVA model is presented as an illustration.

Keywords: Categorical; Data; Dependence; DNA; Genomics; Hamming; distance; Orthogonal; system; Permutation; measure; Second-order; asymptotics; Second-order; decomposability (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (6)

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