李启寨 中国科学院数学与系统科学研究院 研究员

地点：腾讯会议：990-305-586

时间：2025年9月30日 14:30-16:30

报告题目：

Gaussian multiplier bootstrap procedure for the kth largest coordinate of high-dimensional statistics.

摘要: We consider the problem of Gaussian and bootstrap approximations for the distribution of the κth-largest statistic in high dimensions. This statistic, defined as the κth-largest component of the sum of independent random vectors, is critical in numerous high-dimensional estimation and testing problems. Such a problem has been studied previously for κ = 1 (i.e., maxima). However, in many applications, a general κ ≥ 1 is of great interest, which is addressed in this paper. By invoking the iterative randomized Lindeberg method, the paper provides bounds for the errors in distributional approximations. These bounds generalize existing results and extend the applicability to a wider range of bootstrap methods. All these results allow the dimension p of random vectors to be as large as or much larger than the sample size n. Extensive simulation results and real data analysis demonstrate the effectiveness and advantages of the Gaussian multiplier bootstrap procedure.

简介： 中国科学院数学与系统科学研究院 研究员，系统科学研究所副所长；2001年本科毕业于中国科学技术大学，2006年博士毕业于中国科学院数学与系统科学研究院，2006-2009年在美国国立卫生健康研究院(NIH)国家癌症研究所(NCI)从事博士后研究；2011获中国科学院卢嘉锡青年人才奖，2015年获中国工业与应用数学学会优秀青年学者奖，2016年当选国际统计学会推选会员(ISI Elected Member), 2017年获国家优秀青年科学基金，2020年当选美国统计学会会士(ASA Fellow)，2023年获国家杰出青年科学基金；研究方向：生物医学统计、遗传统计、复杂数据建模与推断等；在Nature Genetics, Science Advances, Angewandte Chemie-International Edition, Cancer Research, American Journal of Human Genetics, Bioinformatics, IEEE TPAMI, Psychometrika, JASA, JRSSB, Biometrics等期刊发表SCI论文120余篇；现任中国数学会常务理事、中国现场统计研究会常务理事等。