题目：Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations

主讲人：北京大学 姚方教授

主持人：统计学院 常晋源教授

时间：2021年10月8日（周五）上午9:30-10:30

地点：仁和春天酒店和贵厅

报告摘要：

A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations  derived from sparsely observed Riemannian functional data, while the covariance vector bundle provides a rigorous mathematical foundation for formulating such smoothing problems. The parallel transport and the bundle metric together make it possible to measure fidelity of fit to the covariance function. They also play a critical role in quantifying the quality of estimators for the covariance function. As an illustration, based on the proposed framework, we develop a local linear smoothing estimator for the covariance function, analyze its theoretical properties, and provide numerical demonstration via simulated and real datasets.  The intrinsic feature of the framework makes it applicable to not only Euclidean submanifolds but also manifolds without a canonical ambient space.

主讲人简介：

姚方，北京大学教授, 北大统计科学中心主任，数理统计学会（IMS）Fellow，美国统计学会（ASA）Fellow。2000年本科毕业于中国科技大学统计专业，2003取得加利福尼亚大学戴维斯分校统计学博士学位，曾任职于多伦多大学统计科学系终身教授。现担任Canadian Journal of Statistics的主编，至今担任9个国际统计学核心期刊编委，包括统计学顶级期刊Journal of the American Statistical Association和Annals of Statistics。