Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA

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Show simple item record Wang, Haiyan Akritas, Michael G. 2011-10-13T14:37:28Z 2011-10-13T14:37:28Z 2011-10-13
dc.description.abstract In this paper, we develop the asymptotic theory for hypotheses testing in high-dimensional analysis of variance (HANOVA) when the distributions are completely unspecifed. Most results in the literature have been restricted to observations of no more than two-way designs for continuous data. Here we formulate the local alternatives in terms of departures from the null distribution so that the responses can be either continuous or categorical. The asymptotic theory is presented for testing of main factor and interaction effects of up to order three in unbalanced designs with heteroscedastic variances and arbitrary number of factors. The test statistics are based on quadratic forms whose asymptotic theory is derived under non-classical settings where the number of variables is large while the number of replications may be limited. Simulation results show that the present test statistics perform well in both continuous and discrete HANOVA in type I error accuracy, power performance, and computing time. The proposed test is illustrated with a gene expression data analysis of Arabidopsis thaiana in response to multiple abiotic stresses. en_US
dc.relation.uri en_US
dc.subject Neymann-Scott problem en_US
dc.subject Nonparametric hypotheses en_US
dc.subject Asymptotic distribution theory of quadratic forms en_US
dc.subject Projection method en_US
dc.subject Local alternatives en_US
dc.title Asymptotically distribution free tests in heteroscedastic unbalanced high dimensional ANOVA en_US
dc.type Article (author version) en_US 2011 en_US
dc.citation.doi doi:10.5705/ss.2009.061 en_US
dc.citation.epage 1377 en_US
dc.citation.issue 3 en_US
dc.citation.jtitle Statistica Sinica en_US
dc.citation.spage 1341 en_US
dc.citation.volume 21 en_US
dc.contributor.authoreid hwang en_US

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