We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling’s classical T2 test does not work for this “large p, small n” situation. The proposed test does not require explicit conditions in the relationship between the data dimension and sample size. This offers much flexibility in analyzing high-dimensional data. An application of the proposed test is in testing significance for sets of genes which we demonstrate in an empirical study on a leukemia data set.
"A two-sample test for high-dimensional data with applications to gene-set testing." Ann. Statist. 38 (2) 808 - 835, April 2010. https://doi.org/10.1214/09-AOS716