Institute of Mathematical Statistics Lecture Notes - Monograph Series

Local polynomial regression on unknown manifolds

Peter J. Bickel and Bo Li

Full-text: Open access

Abstract

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

Source
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

Dates
First available in Project Euclid: 4 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196794952

Digital Object Identifier
doi:10.1214/074921707000000148

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

Keywords
local polynomial regression manifolds

Rights
Copyright © 2007, Institute of Mathematical Statistics

Citation

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. https://projecteuclid.org/euclid.lnms/1196794952


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