报告题目：Cross Projection Test For High-Dimensional Mean Vectors

报告人：崔恒建 教授 （首都师范大学）

报告时间：2024年1月18日上午 9:30-10:30

报告地点：学院会议室213

报告摘要: A cross projection test (CPT) technique for a one-sample vector in a high-dimensional setting is introduced. To overcome the problems caused by the curse of dimensionality, we construct test statistics by employing a projection test to project high-dimensional samples into one-or multi-dimensional directions. First, we randomly split the sample into two groups. We then find the p projection directions from a sample covariance matrix of the first group of samples. The second group is used to construct a projection statistic and perform the test. Second, we find the projection directions by exchanging the order of the two groups of samples, and we perform the test again to obtain another test statistic. Finally, we construct the CPT statistic by adding the two asymptotically uncorrelated test statistics together using the cross projection technique, such that the information from the two independent split samples can be fully utilized. The simulation results show that our proposed cross projection test controls the type I error well, and it is more powerful than the existing mean tests for some covariance matrix structures. Meanwhile, after applying the power enhancement technique, the CPT method performs non-trivially in general cases, especially for testing against sparse alternatives. A real gene-data analysis illustrates that the performance of our CPT is quite well.

报告人简介：崔恒建现为首都师范大学教授，博士生导师，中国科协第十届全委会委员，曾任国务院学位委员会学科评议组专家。中国科学院系统科学研究所博士毕业。在大数据统计建模、高维统计数据分析及其稳健统计理论和方法、统计机器学习、金融统计、以及质量管理等领域取得过许多重要的研究成果，发表论文180余篇，其中包括发表在国际顶级的统计和计量经济学杂志JASA、AoS、JRSS(B)、Biometrika和JoE上。主持国家自然科学基金重点项目、杰青（B）项目以及多项面上项目、主要参加教育部重大科研基金项目、科技部863等项目。现担任《数学学报》和《应用数学学报》中、英文版以及STARF编委；中国现场统计研究会副理事长，北京应用统计学会会长，国际数理统计学会（中国分会）常务理事。曾获得教育部高等学校科学技术奖-自然科学奖二等奖；全国统计科学研究优秀成果奖一等奖等。