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

arXiv: https://arxiv.org/abs/1904.07416 · HTML: https://mlsanity.com/paper/1904.07416/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [Sparse Signal Detection in Heteroscedastic Gaussian Sequence Models: Sharp Minimax Rates](https://mlsanity.com/paper/2211.08580/) (2022)

## Abstract (arXiv)

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 based on a nontrivial extension of the one-sample central limit theorem (Chernozhukov et al., 2017) 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.