讲座编号：jz-yjsb-2022-y027
讲座题目：Functional data analysis with covariate-dependent mean and covariance structures
主 讲 人：林华珍 教授 西南财经大学
讲座时间：2022年6月30日（星期四）下午14:00
讲座地点：腾讯会议，会议ID:275 671 716
参加对象：数学与统计学院全体教师及研究生
主办单位：数学与统计学院、研究生院
主讲人简介：
林华珍，西南财经大学教授，统计研究中心主任。国际数理统计学会IMS-fellow，主要研究方向为非参数方法、转换模型、生存数据分析、函数型数据分析、潜变量分析、时空数据分析。研究成果发表在包括国际统计学四大顶级期刊AoS、JASA、JRSSB、Biometrika和计量经济学顶级期刊JOE及JBES上。先后多次主持国家基金项目，包括国家杰出青年基金及自科重点项目。林华珍教授是国际IMS-China、IBS-CHINA及ICSA-China委员，中国现场统计研究会数据科学与人工智能分会理事长，第九届全国工业统计学教学研究会副会长，中国现场统计研究会多个分会的副理事长。先后是国际统计学权威期刊《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， 国内权威或核心学术期刊《数学学报》（英文）、《应用概率统计》、《系统科学与数学》、《数理统计与管理》编委会编委。
主讲内容：
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.