统计与数据科学系系列学术报告之四百九十二期

时间：2025年11月13日（周四）16:00-17:00

主持人：复旦大学管理学院统计与数据科学系章玮助理教授

地点：史带楼503室

报告人：胡晓玉教授

西安交通大学

题目：Two-sample distribution tests in high dimensions via max-sliced Wasserstein distance and bootstrapping

摘要： Two-sample hypothesis testing is a fundamental statistical problem for inference about two populations. We construct a novel test statistic to detect high-dimensional distributional differences based on the max-sliced Wasserstein distance to mitigate the curse of dimensionality. By exploiting an intriguing link between the distance and suprema of empirical processes, we develop an effective bootstrapping procedure to approximate the null distribution of the test statistic. One distinctive feature of the proposed test is the ability to construct simultaneous confidence intervals for the max-sliced Wasserstein distances of projected distributions of interest. This enables, not only the detection of global distributional differences, but also the identification of significantly different marginal distributions between two populations, without the need for additional tests. We establish the convergence of Gaussian and bootstrap approximations of the proposed test, based on which we show that the test is asymptotically valid and powerful as long as the considered max-sliced Wasserstein distance is adequately large. The merits of the proposed approach are illustrated via simulated and real data examples.

个人简介：胡晓玉，西安交通大学数学与统计学院教授，博士生导师，入选校内青年拔尖人才A类支持计划。博士毕业于北京大学，曾在新加坡国立大学统计与数据科学系从事博士后研究。主要研究方向为高维统计推断，函数型数据分析和迁移学习等。相关研究成果发表在JASA、Biometrika 和 NeurIPS等学术期刊与会议。