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June 2020 Distribution and correlation-free two-sample test of high-dimensional means
Kaijie Xue, Fang Yao
Ann. Statist. 48(3): 1304-1328 (June 2020). DOI: 10.1214/19-AOS1848


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 (Ann. Probab. 45 (2017) 2309–2352) 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 have demonstrated favorable numerical performance over existing methods.


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Kaijie Xue. Fang Yao. "Distribution and correlation-free two-sample test of high-dimensional means." Ann. Statist. 48 (3) 1304 - 1328, June 2020.


Received: 1 October 2018; Revised: 1 January 2019; Published: June 2020
First available in Project Euclid: 17 July 2020

zbMATH: 07241592
MathSciNet: MR4124324
Digital Object Identifier: 10.1214/19-AOS1848

Primary: 62F05 , 62H05

Keywords: High-dimensional central limit theorem , Kolmogorov distance , multiplier bootstrap , power function

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.48 • No. 3 • June 2020
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