報告題目: 一類Chatterjee相關系數及其應用
報告專家：李啟寨 研究員，中國科學院數學與系統科學研究院。
時 間： 2024年3月29日10：20—11：20
地 點： 9-122會議室
報告摘要: Quantifying the strength of functional dependence between random scalars X and Y is an important statistical problem. While many existing correlation coefficients excel in identifying linear or monotone functional dependence, they fall short in capturing general non-monotone functional relationships. In response, we propose a family of correlation coefficients ξ(h,F) , characterized by a continuous bivariate function h and a c.d.f. function F. By offering a range of selections for h and F, ξ (h,F) encompasses a diverse class of novel correlation coefficients, while also incorporates the Chatterjee’s correlation coefficient (Chatterjee, 2021) as a special case. We prove that ξ (h,F) converges almost surely to a deterministic limit ξ (h,F) as sample size n approaches infinity. In addition, under appropriate conditions imposed on h and F, the limit ξ(h,F) satisfies the three appealing properties: (P1). It belongs to the range of [0, 1]; (P2). it equals 1 if and only if Y is a measurable function of X; and (P3). it equals 0 if and only if Y is independent of X. As amplified by our numerical experiments, our proposals provide practitioners with a variety of options to choose the most suitable correlation coefficient tailored to their specific practical needs.
專家簡介： 李啟寨，中國科學院數學與系統科學研究院研究員，國家杰出青年科學基金獲得者，美國統計學會會士(ASA Fellow)，國際統計學會推選會員(ISI Elected Member)；2001年本科畢業于中國科學技術大學，2006年博士畢業于中國科學院數學與系統科學研究院，2006-2009年在美國國家癌癥研究所(NCI)從事博士后研究；研究方向包括生物醫學統計、遺傳統計和復雜數據推斷等，在Nature Genetics, Science Advances, Angewandte Chemie-International Edition, Cancer Research, American Journal of Human Genetics, Bioinformatics, JASA, JRSSB, Biometrics等期刊發表SCI論文110余篇；現任中國數學會常務理事、中國現場統計研究會常務理事等。
作者：王子軒；編輯：劉鹍；審核：郭暉；上傳：郭敏。
