报告题目：Nonparametric two-sample tests of high dimensional mean vectors via random integration

报告时间：2024年9月18日下午15：00

会议链接：https://meeting.tencent.com/dm/DuxGuStbt7pN

会议 ID：961-799-845

主办单位：数学与统计学院

报告人：姜云卢

报告人简介：姜云卢，暨南大学经济学院统计学系教授、博士生导师。博士毕业于中山大学。目前的主要研究包括：稳健统计、高维数据分析、变量选择。在JASA、Technometrics、Statistica Sinica等国际顶级学术期刊上发表SCI论文40余篇，其中1篇论文入选ESI高被引论文；先后访问了昆士兰大学、香港大学、澳门大学和南方科技大学等多所知名高校；2016年和2020年分别入选暨南双百英才计划暨南杰青第二层次和第一层次；2014年入选广东省高等学校“千百十工程”第八批培养对象；2010年获第八次广东省统计科研优秀成果奖一等奖（排第三）；并担任JASA、CSDA等国际权威统计期刊的审稿人；主持和参与十多项国家级和省部级等科研项目。

摘要：Testing the equality of the means in two samples is a fundamental statistical inferential problem. Most of the existing methods are based on the sum-of-squares or supremum statistics. They are possibly powerful in some situations, but not in others, and they do not work in a unified way. Using random integration of the difference, we develop a framework that includes and extends many existing methods,  especially in high-dimensional settings, without restricting the same covariance matrices or sparsity. Under a general multivariate model, we can derive the asymptotic properties of the proposed test statistic without specifying a relationship between the data dimension and sample size explicitly. Specifically, the new framework allows us to better understand the test's properties and select a powerful procedure accordingly. For example, we prove that our proposed test can achieve the power of 1 when nonzero signals in the true mean differences are weakly dense with nearly the same sign. In addition, we delineate the conditions under which the asymptotic relative Pitman efficiency of our proposed test to its competitor is greater than or equal to 1. Extensive numerical studies and a real data example demonstrate the potential of our proposed test.