We consider 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-squared 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. Using ROC curves generated from synthetic data, we demonstrate superior performance against competing tests in the parameter regimes anticipated by our theoretical results.
Title
A More Powerful Two-Sample Test in High Dimensions using Random Projection
Published
2014-04-09
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2014-28
Type
Text
Extent
29 p
Archive
The Engineering Library
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