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We propose a two-sample test for high-dimensional means that requires neitherdistributional nor correlational assumptions, besides some weak conditions onthe moments and tail properties of the elements in the random vectors. Thistwo-sample test based on a nontrivial extension of the one-sample central limittheorem (Chernozhukov et al., 2017) provides a practically useful procedurewith rigorous theoretical guarantees on its size and power assessment. Inparticular, the proposed test is easy to compute and does not require theindependently and identically distributed assumption, which is allowed to havedifferent distributions and arbitrary correlation structures. Further desiredfeatures include weaker moments and tail conditions than existing methods,allowance for highly unequal sample sizes, consistent power behavior underfairly general alternative, data dimension allowed to be exponentially highunder the umbrella of such general conditions. Simulated and real data examplesare used to demonstrate the favorable numerical performance over existingmethods.

Distribution and correlation free two-sample test of high-dimensional means