22 November 2022
  • Title: Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations
  • Date: 9:00pm US East time, Saturday, 11/26/2022
  • Date: 10:00am Beijing time, Sunday, 11/27/2022
  • Zoom ID:933 1613 9423
  • Zoom PWD:416262

Title: Intrinsic Riemannian Functional Data Analysis for Sparse Longitudinal Observations


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.


Fang Yao 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.



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Previous Talk from Dr.Liyan Xie, Chinese University of Hong Kong

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