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**Distribution and correlation-free two-sample test of high-dimensional means.**
*(English)*
Zbl 1454.62157

The authors propose a two-sample test for comparing 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 called “distribution and correlation-free (DCF) two-sample mean test” is based on a nontrivial
extension of the one-sample central limit theorem. The proposed test does not require the independently and identically distributed assumption. Weaker moments and tail conditions are posed than in the existing methods. The test allows highly unequal sample sizes. It has consistent power behavior under fairly general alternative. Simulated and real data examples demonstrate good numerical performance compared with existing methods.

Reviewer: Pavel Stoynov (Sofia)

### MSC:

62H05 | Characterization and structure theory for multivariate probability distributions; copulas |

62H15 | Hypothesis testing in multivariate analysis |

62F05 | Asymptotic properties of parametric tests |

60F05 | Central limit and other weak theorems |

### Keywords:

high-dimensional central limit theorem; Kolmogorov distance; multiplier bootstrap; power function
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\textit{K. Xue} and \textit{F. Yao}, Ann. Stat. 48, No. 3, 1304--1328 (2020; Zbl 1454.62157)

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