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学术报告

Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations

林振华 Presidential Young Professor

（新加坡国立大学）

报告时间： 2021年11月22日 (星期一) 上午10：00-11：00

腾讯会议 ID：815 227 940

报告摘要：A novel 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 the 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.

报告人简介：林振华是新加坡国立大学统计与应用概率系的Presidential Young Professor。他于2008年获得复旦大学学士学位，2010和2013年获得西蒙弗雷泽大学硕士学位， 2017年获得多伦多大学博士学位。2017-2019年期间，他在加州大学戴维斯分校从事博士后工作。他的研究兴趣主要为函数型数据分析，高维数据分析和非欧氏数据分析。目前已有多项工作发表在统计学顶级期刊The Annals of Statistics（AOS）、Journal of American Statistical Association(JASA)，Biometrika等。详情请见其个人链接：https://blog.nus.edu.sg/zhenhua/

邀请人： 陈迪荣