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Functional Regression on Manifold with Contamination

Banff International Research Station for Mathematical Innovation and Discovery

We propose 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 noise/sampling 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 favourable finite sample performance relative to commonly used methods via simulated and real data examples.

Mathematics; Statistics; Partial differential equations

video/mp4

Author affiliation: University of Toronto

2018-03-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64972

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/