关于两样本Behrens-Fisher问题，该研究在高维检验问题中取得新的进展。在此问题中，Chen & Qin (2010)所提出的检验统计量具有广泛的影响力。然而，在本项工作之前，如何在一般的条件下控制住此统计量的检验水平是一个悬而未决的问题。本文作者针对Chen & Qin (2010)的检验统计量，给出了统计量在不同的条件下所有可能的分布，提出了一种新的近似随机化检验方法，并给出其理论性质。理论结果表明，新的随机化检验方法在非常一般的条件下即可在渐近意义下控制住检验水平。特别的，新提出的方法不需要对两样本的协方差矩阵施加任何假设。对协方差矩阵条件放松，极大拓展了该方法在实际问题中的应用。
论文题目：
An approximate randomization test for the high-dimensional two-sample Behrens–Fisher problem under arbitrary covariances
文章摘要：
This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of? is proposed. The asymptotic behaviour of the test statistic as well as the randomized statistic is studied under weak conditions. In our theoretical framework, observations are not assumed to be identically distributed even within groups. No condition on the eigenstructure of the covariance matrices is imposed. And the sample sizes of the two groups are allowed to be unbalanced. Under general conditions, all possible asymptotic distributions of the test statistic are obtained. We derive the asymptotic level and local power of the approximate randomization test procedure. Our theoretical results show that the proposed test procedure can adapt to all possible asymptotic distributions of the test statistic, always has correct test level asymptotically, and has good power behaviour. Our numerical experiments show that the proposed test procedure has favourable performance compared with several alternative test procedures.
作者介绍
王睿，本科和博士毕业于北京理工大学，于2020年取得统计学博士学位，博士导师是徐兴忠教授。王睿到中国人民大学统计学院从事师资博士后，合作导师是许王莉教授。王睿主要从事高维统计、随机化算法、计算机视觉等领域的研究。目前已在Biometrika、Statistica Sinica、Journal of Multivariate Analysis、AISTATS等期刊和会议发表多篇学术论文。
许王莉（通讯作者），中国人民大学统计学院教授、应用统计科学研究中心研究员。现任中国人民大学明理书院副院长、统计学院生物统计与流行病学系系主任。主要研究方向包括高维模型检验、缺失数据分析、生物医学数据分析、抽样设计等。
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