講座編號(hào)：jz-yjsb-2022-y027
講座題目：Functional data analysis with covariate-dependent mean and covariance structures
主 講 人：林華珍 教授 西南財(cái)經(jīng)大學(xué)
講座時(shí)間：2022年6月30日（星期四）下午14:00
講座地點(diǎn)：騰訊會(huì)議，會(huì)議ID:275 671 716
參加對(duì)象：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院全體教師及研究生
主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、研究生院
主講人簡介：
林華珍，西南財(cái)經(jīng)大學(xué)教授，統(tǒng)計(jì)研究中心主任。國際數(shù)理統(tǒng)計(jì)學(xué)會(huì)IMS-fellow，主要研究方向?yàn)榉菂?shù)方法、轉(zhuǎn)換模型、生存數(shù)據(jù)分析、函數(shù)型數(shù)據(jù)分析、潛變量分析、時(shí)空數(shù)據(jù)分析。研究成果發(fā)表在包括國際統(tǒng)計(jì)學(xué)四大頂級(jí)期刊AoS、JASA、JRSSB、Biometrika和計(jì)量經(jīng)濟(jì)學(xué)頂級(jí)期刊JOE及JBES上。先后多次主持國家基金項(xiàng)目，包括國家杰出青年基金及自科重點(diǎn)項(xiàng)目。林華珍教授是國際IMS-China、IBS-CHINA及ICSA-China委員，中國現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)數(shù)據(jù)科學(xué)與人工智能分會(huì)理事長，第九屆全國工業(yè)統(tǒng)計(jì)學(xué)教學(xué)研究會(huì)副會(huì)長，中國現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)多個(gè)分會(huì)的副理事長。先后是國際統(tǒng)計(jì)學(xué)權(quán)威期刊《Biometrics》、《Scandinavian Journal of Statistics》、《Journal of Business & Economic Statistics》、《Canadian Journal of Statistics》、 《Statistics and Its Interface》、《Statistical Theory and Related Fields》的Associate Editor， 國內(nèi)權(quán)威或核心學(xué)術(shù)期刊《數(shù)學(xué)學(xué)報(bào)》（英文）、《應(yīng)用概率統(tǒng)計(jì)》、《系統(tǒng)科學(xué)與數(shù)學(xué)》、《數(shù)理統(tǒng)計(jì)與管理》編委會(huì)編委。
主講內(nèi)容：
Functional data analysis has emerged as a powerful tool in response to the ever increasing resources and efforts devoted to collecting information about response curves or anything varying over a continuum. However, limited progress has been made to link the covariance structure of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing the variances of the random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions which govern the patterns of variation across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure, which combines regularization and B-spline smoothing, for model selection and estimation, and establish the convergence rate and asymptotic normality for the proposed estimators. The utility of the method is demonstrated via simulations as well as an analysis of the Avon Longitudinal Study of Parents and Children on parental effects on the growth curves of their offspring, which yields biologically interesting results.