Large-Scale Multiple Testing of Correlations.

Multiple testing of correlations arises in many applications including gene coexpression network analysis and brain connectivity analysis. In this paper, we consider large scale simultaneous testing for correlations in both the one-sample and two-sample settings. New multiple testing procedures are proposed and a bootstrap method is introduced for estimating the proportion of the nulls falsely rejected among all the true nulls. The properties of the proposed procedures are investigated both theoretically and numerically. It is shown that the procedures asymptotically control the overall false discovery rate and false discovery proportion at the nominal level. Simulation results show that the methods perform well numerically in terms of both the size and power of the test and it significantly outperforms two alternative methods. The two-sample procedure is also illustrated by an analysis of a prostate cancer dataset for the detection of changes in coexpression patterns between gene expression levels.