Are a set of microarrays independent of each other?

Abstract

Having observed an $m\times n$ matrix $X$ 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 $X$ record expression levels for $m$ different genes, often highly correlated, while the columns represent $n$ 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 $X$ interact with each other in a way that complicates test procedures, essentially by reducing the accuracy of the relevant estimators.

arXiv commentPublished in at http://dx.doi.org/10.1214/09-AOAS236 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• In silico prediction of protein-protein interactions in human macrophages
• Size, power and false discovery rates
• Microarrays, Empirical Bayes and the Two-Groups Model

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