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arXiv · 0910.1426

Are a set of microarrays independent of each other?

Bradley Efron
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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.

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Bradley Efron. 2009-10-08. Are a set of microarrays independent of each other?. https://doi.org/10.1214/09-aoas236

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