Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)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. (C) 2009 Elsevier Inc. All rights reserved.100816451656Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAEP-UNICAMP [412/04]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [03/10105_2, 06/04897_1]FAEP-UNICAMP [412/04]CNPq [474329/2004_6]