珠海数学杰出学者讲座第37讲-A Unified PCA Framework for Irregularly Observed Functional Time Series

讲座题目：A Unified PCA Framework for Irregularly Observed Functional Time Series
讲座时间 Datetime: 2024年10月18日，周五，15：00开始
地点 Venue: 海琴二号457
报告人Speaker: 黄辉 教授
单位 Affiliation: 中国人民大学
主持人 Host：赵育林 教授
报告摘要 Abstract:
Abstract: Irregularly observed functional time series (FTS) are increasingly available in many real-world applications. To analyze FTS, it's crucial to account for both serial dependencies and the irregularly observed nature of functional data. However, existing methods for FTS often rely on specific model assumptions in capturing serial dependencies, or cannot handle the irregular observational scheme of functional data.To solve these issues, one can perform dimension reduction on FTS via functional principal component analysis (FPCA) or dynamic FPCA. Nonetheless, these two methods may either be not theoretically optimal or too redundant to represent serially dependent functional data. In this article, we introduce a novel dimension reduction method for FTS based on the framework of dynamic FPCA. Through a new concept called optimal functional filters, we unify the theories of FPCA and dynamic FPCA, providing a parsimony and optimal representation for FTS adapting to its serial dependence structure. This framework is referred to as principal analysis via dependency-adaptivity (PADA). Under a hierarchical Bayesian model, we establish an estimation procedure for dimension reduction via PADA. Our method can be used for both sparsely and densely observed FTS, and is capable of predicting future functional data. We investigate the theoretical properties of PADA and demonstrate its effectiveness through extensive simulation studies. We illustrate our method via dimension reduction and prediction of daily PM2.5 data.

报告人简介：
黄辉博士，2004年于中国科学技术大学获得统计学学士学位，2010年于马里兰大学巴郡分校获得统计学博士学位， 并先后在耶鲁大学和迈阿密大学从事博士后研究工作，目前为中国人民大学统计学院教授、博士生导师。2015年入选国家“青年海外高层次人才引进计划”；研究方向主要集中于空间统计学、时空数据分析、空间流行病等领域；在国际顶级统计学、交叉学科期刊发表论文多篇，先后主持并完成基金委青年项目、面上项目和科技部国家重点研发计划子课题，正主持基金委重点项目子课题，并参与其他重大项目多项。