Functional regression on the manifold with contamination

• 成果类型: Article
• 署名作者: Lin, Zhenhua; Yao, Fang
• 署名单位: National University of Singapore; Peking University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa041
• 发表日期: 2021
• 页码: 167181
• 关键词: Principal component analysis; local linear-regression; extrinsic sample means; RIEMANNIAN-MANIFOLDS; models; SPARSE

摘要

We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold, but is observable only in an infinite-dimensional space. Contamination of the predictor due to discrete or noisy measurements is also accounted for. By using functional local linear manifold smoothing, the proposed estimator enjoys a polynomial rate of convergence that adapts to the intrinsic manifold dimension and the contamination level. This is in contrast to the logarithmic convergence rate in the literature of functional nonparametric regression. We also observe a phase transition phenomenon related to the interplay between the manifold dimension and the contamination level. We demonstrate via simulated and real data examples that the proposed method has favourable numerical performance relative to existing commonly used methods.