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.Comment: Published 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