李启寨，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国家癌症研究所从事博士后研究， 2016年当选国际统计学会推选会员(ISI Elected Member), 2020年当选美国统计学会会士(ASA Fellow)。研究方向：生物医学统计、遗传统计、复杂数据推断等；在Nature Genetics, Science Advances, Angewandte Chemie-International Edition, Cancer Research, AJHG, Bioinformatics,IEEE TPAMI, Psychometrika, JASA, JRSSB, Biometrics等期刊发表SCI论文130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。

   报告摘要：We consider the problem of Gaussian approximation for the κth coordinate of a sum of high-dimensional random vectors. 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. We make four contributions: 1) we first show that the distribution of the κth coordinate of a sum of random vectors,  can be approximated by that of Gaussian random vectors and derive their Kolmogorov’s distributional difference bound; 2) we provide the theoretical justification for estimating the distribution of the κth coordinate of a sum of random vectors using a Gaussian multiplier procedure, which multiplies the original vectors with i.i.d. standard Gaussian random variables; 3) we extend the Gaussian approximation result and Gaussian multiplier bootstrap procedure to a more general case where κ diverges; 4) we further consider the Gaussian approximation for a square sum of the first d largest coordinates. All these results allow the dimension p of random vectors to be as large as or much larger than the sample size n.