A More Powerful Two-sample Test in High Dimensions Using Random Projection

Miles Lopes, University of California, Berkeley

We study the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. This problem arises in many applications, such as the problem of detecting differential expression of gene pathways. Specifically, we propose a new test statistic for the two-sample test of means that integrates a random projection with the classical Hotelling T^2 statistic. Working under a high-dimensional framework with (p,n) tending to infinity, we first derive an asymptotic power function for our test and then provide sufficient conditions for it to achieve greater power than other state-of-the-art tests. Lastly, using ROC curves generated from simulated data, we demonstrate superior performance with competing tests in the parameter regimes anticipated by our theoretical results.

Abstract Author(s): Miles Lopes, Laurent Jacob, Martin Wainwright