報(bào)告題目: 一類(lèi)Chatterjee相關(guān)系數(shù)及其應(yīng)用
報(bào)告專(zhuān)家：李啟寨 研究員，中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院。
時(shí) 間： 2024年3月29日10：20—11：20
地 點(diǎn)： 9-122會(huì)議室
報(bào)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(zhuān)家簡(jiǎn)介： 李啟寨，中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院研究員，國(guó)家杰出青年科學(xué)基金獲得者，美國(guó)統(tǒng)計(jì)學(xué)會(huì)會(huì)士(ASA Fellow)，國(guó)際統(tǒng)計(jì)學(xué)會(huì)推選會(huì)員(ISI Elected Member)；2001年本科畢業(yè)于中國(guó)科學(xué)技術(shù)大學(xué)，2006年博士畢業(yè)于中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院，2006-2009年在美國(guó)國(guó)家癌癥研究所(NCI)從事博士后研究；研究方向包括生物醫(yī)學(xué)統(tǒng)計(jì)、遺傳統(tǒng)計(jì)和復(fù)雜數(shù)據(jù)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(fā)表SCI論文110余篇；現(xiàn)任中國(guó)數(shù)學(xué)會(huì)常務(wù)理事、中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)常務(wù)理事等。
作者：王子軒；編輯：劉鹍；審核：郭暉；上傳：郭敏。
