講座編號：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 西南財經大學
講座時間：2022年6月30日（星期四）下午14:00
講座地點：騰訊會議，會議ID:275 671 716
參加對象：數學與統計學院全體教師及研究生
主辦單位：數學與統計學院、研究生院
主講人簡介：
林華珍，西南財經大學教授，統計研究中心主任。國際數理統計學會IMS-fellow，主要研究方向為非參數方法、轉換模型、生存數據分析、函數型數據分析、潛變量分析、時空數據分析。研究成果發表在包括國際統計學四大頂級期刊AoS、JASA、JRSSB、Biometrika和計量經濟學頂級期刊JOE及JBES上。先后多次主持國家基金項目，包括國家杰出青年基金及自科重點項目。林華珍教授是國際IMS-China、IBS-CHINA及ICSA-China委員，中國現場統計研究會數據科學與人工智能分會理事長，第九屆全國工業統計學教學研究會副會長，中國現場統計研究會多個分會的副理事長。先后是國際統計學權威期刊《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， 國內權威或核心學術期刊《數學學報》（英文）、《應用概率統計》、《系統科學與數學》、《數理統計與管理》編委會編委。
主講內容：
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.