题    目：Multivariate two-sample tests via random projection

主讲人：杜江 教授

单    位：北京工业大学

时    间：2025年5月24日 15:30

地    点：学院北研教室

摘    要： The two-sample test problem is a fundamental problem in statistical inference that attempts to test whether two probability measures are different based on corresponding samples. Consequently, many statistical methods have been proposed when random vectors are multivariate or even high-dimensional. For this problem, we introduce a randomly projected maximum mean discrepancy (MMD) in a reproducing kernel Hilbert space to characterize the distance between the distributions of two random vectors. The multivariate random vectors are projected onto univariate random variables and projected MMD statistics are constructed. The collection of projected MMD indexed by the unit sphere, and hence we treat it as the U-process. Theorems include the asymptotic theory of test statistics under the null hypothesis and the alternative hypothesis. Combining continuous mapping theory with projected MMD statistics, a class of test statistics is proposed, which includes the Cramer-von Mises and Kolmogorov-Smirnov methods as special cases. Since the limit null distribution of the test statistic depends on the data generation process, we apply the permutation test procedure to determine a critical value. Furthermore, the empirical size and power of the test statistics are evaluated by numerical simulations. Finally, we illustrate our method by applying it to real data sets with two-sample problem.

简    介：杜江，北京工业大学数学统计学与力学学院，教授，博士生导师。主持国家自然科学基金项目2项。已在国内外学术刊物上发表论文50 余篇，其中40余篇被SCI检索。研究方向为空间数据分析、模型检验、高维数据分析等。