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Functional Regression with Unknown Manifold Structures

Speaker

Fang Yao, University of Toronto,Peking University

Time

2017.04.27 15:00-16:00

Venue

Large Conference Room, Math Building

Abstract

Statistical methods that adapt to unknown population structures are attractive due to both practical and theoretical advantages over their non-adaptive counterparts. We contribute to adaptive modelling of functional regression, where challenges arise from the infinite dimensionality of functional predictor in the underlying space. We are interested in the scenario that the predictor process lies in a potentially nonlinear manifold that is intrinsically finite-dimensional and embedded in an infinite-dimensional functional space. By a novel functional regression approach built upon 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, which 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.