李啟寨，中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院 研究員，系統(tǒng)科學(xué)研究所副所長；2001年本科畢業(yè)于中國科學(xué)技術(shù)大學(xué)，2006年博士畢業(yè)于中國科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院，2006-2009年在美國國立衛(wèi)生健康研究院國家癌癥研究所從事博士后研究， 2016年當選國際統(tǒng)計學(xué)會推選會員(ISI Elected Member), 2020年當選美國統(tǒng)計學(xué)會會士(ASA Fellow)。研究方向：生物醫(yī)學(xué)統(tǒng)計、遺傳統(tǒng)計、復(fù)雜數(shù)據(jù)推斷等；在Nature Genetics, Science Advances, Angewandte Chemie-International Edition, Cancer Research, AJHG, Bioinformatics,IEEE TPAMI, Psychometrika, JASA, JRSSB, Biometrics等期刊發(fā)表SCI論文130余篇；現(xiàn)任中國數(shù)學(xué)會常務(wù)理事、中國現(xiàn)場統(tǒng)計研究會常務(wù)理事等。
報告摘要：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.
