Are a set of microarrays independent of each other?
Bradley Efron
Source: Ann. Appl. Stat. Volume 3, Number 3
(2009), 922-942.
Abstract
Having observed an m×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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Keywords: Total correlation; effective sample size; permutation tests; matrix normal distribution; row and column correlations
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoas/1254773272
Digital Object Identifier: doi:10.1214/09-AOAS236
Zentralblatt MATH identifier: 05758445
Mathematical Reviews number (MathSciNet): MR2750220
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