Title: Functional regression on manifolds with contamination
Authors: Fang Yao - Peking University, University of Toronto (Canada) [presenting]
Zhenhua Lin - University of California, Davis (United States)
Abstract: The focus is on a new perspective on functional regression with a predictor process via the concept of manifold that is intrinsically finite-dimensional and embedded in an infinite-dimensional functional space, where the predictor is contaminated with discrete/noisy measurements. By a method of functional local linear manifold smoothing, we achieve a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the level of sampling/noise contamination with a phase transition phenomenon depending on their interplay. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We demonstrate that the proposed method enjoys favorable finite sample performance relative to commonly used methods via simulated and real data examples.