Abstract:
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) n , 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)n 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)n 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.
About the Speaker:
李启寨，中国科公司数学与系统科学研究院研究员，系统科学研究所副所长，国家杰出青年科学基金获得者(2023), 美国统计学会会士(ASA Fellow, 2020)，国际统计学会推选会员(ISI Elected Member, 2016); 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公司数学与系统科学研究院，2006-2009年在美国国家癌症研究所(NCI)从事博士后研究；研究方向包括生物医学统计、遗传统计和复杂数据推断等，在Nature Genetics, Science Advances, Angewandte Chemie-International Edition, American Journal of Human Genetics, Cancer Research, Bioinformatics, JASA, JRSSB, Biometrics, Biostatistics, Statistics in Medicine等期刊发表SCI论文110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。
