B0290
Title: Intrinsic Riemannian functional data analysis
Authors: Zhenhua Lin - National University of Singapore (Singapore) [presenting]
Lingxuan Shao - Peking University (China)
Fang Yao - Peking University (China)
Abstract: Riemannian functional data, in which functions take values in a nonlinear Riemannian manifold, pose new challenges to functional data analysis. To overcome these challenges, an intrinsic framework to analyze densely/sparsely observed Riemannian functional data is developed. The framework features the following innovative components: a frame-independent covariance operator/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 the 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 mathematical foundation for formulating the smoothing problems. The parallel transport and the bundle metric together make it possible to measure the 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, a local linear smoothing estimator is developed for the covariance function.
