Institute of Mathematical Statistics Lecture Notes - Monograph Series

Local polynomial regression on unknown manifolds

Peter J. Bickel and Bo Li

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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.

Chapter information

Regina Liu, William Strawderman and Cun-Hui Zhang, eds., Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 177-186

First available in Project Euclid: 4 December 2007

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Digital Object Identifier

Primary: 62G08: Nonparametric regression 62H12: Estimation
Secondary: 62G20: Asymptotic properties

local polynomial regression manifolds

Copyright © 2007, Institute of Mathematical Statistics


Bickel, Peter J.; Li, Bo. Local polynomial regression on unknown manifolds. Complex Datasets and Inverse Problems, 177--186, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000148.

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