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In high dimensions, the classical Hotelling's $T^2$ test tends to have lowpower or becomes undefined due to singularity of the sample covariance matrix.In this paper, this problem is overcome by projecting the data matrix ontolower dimensional subspaces through multiplication by random matrices. Wepropose RAPTT (RAndom Projection T-Test), an exact test for equality of meansof two normal populations based on projected lower dimensional data. RAPTT doesnot require any constraints on the dimension of the data or the sample size. Asimulation study indicates that in high dimensions the power of this test isoften greater than that of competing tests. The advantage of RAPTT isillustrated on high-dimensional gene expression data involving thediscrimination of tumor and normal colon tissues.

RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections