Open Access
VOL. 54 | 2007 Local polynomial regression on unknown manifolds
Peter J. Bickel, Bo Li

Editor(s) Regina Liu, William Strawderman, Cun-Hui Zhang

IMS Lecture Notes Monogr. Ser., 2007: 177-186 (2007) DOI: 10.1214/074921707000000148


We reveal the phenomenon that “naive” multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal convergence rate for nonparametric estimation of regression functions belonging to a Sobolev space when the predictor variables live on or close to a lower dimensional manifold.


Published: 1 January 2007
First available in Project Euclid: 4 December 2007

Digital Object Identifier: 10.1214/074921707000000148

Primary: 62G08 , 62H12
Secondary: 62G20

Keywords: local polynomial regression , Manifolds

Rights: Copyright © 2007, Institute of Mathematical Statistics

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