报告题目：Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations

报告时间：2022年2月23日上午10：00

会议链接：https://meeting.tencent.com/dm/jZVuirascOmK

会议 ID：979-798-774

主办单位：数学与统计学院

主讲人：姚方

姚方简介：北京大学讲席教授，北大统计科学中心主任，概率统计系主任。数理统计学会与美国统计学会会士。2000年本科毕业于中国科技大学统计专业，2003获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长聘教授。现担任《加拿大统计学期刊》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《北美统计学会会刊》和 《统计年刊》。

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.