Are a set of microarrays independent of each other?


Having observed an m×nm\times n matrix XX whose rows are possibly correlated, we wish to test the hypothesis that the columns are independent of each other. Our motivation comes from microarray studies, where the rows of XX record expression levels for mm different genes, often highly correlated, while the columns represent nn individual microarrays, presumably obtained independently. The presumption of independence underlies all the familiar permutation, cross-validation and bootstrap methods for microarray analysis, so it is important to know when independence fails. We develop nonparametric and normal-theory testing methods. The row and column correlations of XX interact with each other in a way that complicates test procedures, essentially by reducing the accuracy of the relevant estimators.Comment: Published in at the Annals of Applied Statistics ( by the Institute of Mathematical Statistics (

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    Last time updated on 01/04/2019