报告题目：Functional data analysis with covariate-dependent mean and covariance structures

报告时间：2024年8月3日下午15：00

报告地点：南湖校区老图书馆四楼左侧研究生5-1学习室

主办单位：数学与统计学院/科研处

报告人：林华珍

报告人简介： 林华珍，西南财经大学首席教授、统计研究中心主任，首届新基石研究员，国际数理统计学会IMS-fellow，获得国家级人才称号。主要研究方向为深度学习理论、非参数方法、生存数据分析、函数型数据分析、因子模型、转换模型等。研究成果发表在包括国际统计学四大顶刊JASA、AOS、JRSSB及Biometrika上。先后担任国际7个统计学杂志的Associate Editor，包括JASA、Biometrics、Journal of Business &Economic Statistics、Scandinavian Journal of Statistics、Canadian Journalof Statistics 等，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。现任国际泛华统计学会ICSA 董事会成员,中国现场统计研究会副理事长，中国现场统计研究会数据科学与人工智能分会理事长，全国工业统计学教学研究会副会长。

摘要：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.