Kaijie Xue, University of Toronto
520, Pao Yue-Kong Library
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This two-sample test provides a practically useful procedure with rigorous theoretical guarantees on its size and power assessment. In particular, the proposed test is easy to compute and does not require the independently and identically distributed assumption, which is allowed to have different distributions and arbitrary correlation structures. Further desired features include weaker moments and tail conditions than existing methods, allowance for highly unequal sample sizes, consistent power behavior under fairly general alternative, data dimension allowed to be exponentially high under the umbrella of such general conditions. Simulated and real data examples are used to demonstrate the favorable numerical performance over existing methods.