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September 2009 Are a set of microarrays independent of each other?
Bradley Efron
Ann. Appl. Stat. 3(3): 922-942 (September 2009). DOI: 10.1214/09-AOAS236


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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Bradley Efron. "Are a set of microarrays independent of each other?." Ann. Appl. Stat. 3 (3) 922 - 942, September 2009.


Published: September 2009
First available in Project Euclid: 5 October 2009

zbMATH: 1196.62138
MathSciNet: MR2750220
Digital Object Identifier: 10.1214/09-AOAS236

Keywords: effective sample size , matrix normal distribution , permutation tests , row and column correlations , Total correlation

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.3 • No. 3 • September 2009
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