Biography: Fang Yao(Chinese: 姚方) is Chair Professor in School of Mathematical Sciences, Director of Center for Statistical Science at Peking University. He is a Fellow of IMS and ASA, and an elected member of ISI. He received his B.S. degree in 2000 from University of Science & Technology in China, and his Ph.D. degree in Statistics in 2003 at UC Davis. He was a tenured Full Professor in Statistical Sciences at University of Toronto during 2014-2019. Dr. Yao’s research primarily focuses on functional and longitudinal data, complex structures such as high dimensions and manifolds, and their applications in various disciplines. In 2014, he received the CRM-SSC Prize that recognizes a statistical scientist’s professional accomplishments in research primarily conducted in Canada during the first 15 years after receiving a doctorate. He currently serves as the Editor for Canadian Journal of Statistic, and is/was on editorial boards for nine statistical journals, including Annals of Statistics and Journal of the American Statistical Association.

Title: Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations

Abstract:  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.

Joint work with Lingxuan Shao and Zhenhua Lin.