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Abstract Details

Activity Number: 672
Type: Contributed
Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #305541
Title: A More Powerful Two-Sample Test in High Dimensions Using Random Projection
Author(s): Miles Lopes*+ and Laurent Jacob and Martin J. Wainwright
Companies: University of California at Berkeley and University of California at Berkeley and University of California at Berkeley
Address: 1717 Euclid Ave, Apt. #12, Berkeley, CA, 94709, United States
Keywords: high-dimensional statistics ; hypothesis testing ; two-sample test ; random projection ; gene set testing ; dimension reduction
Abstract:

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. 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.


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