Local polynomial regression on unknown manifolds
Log in :: RSS/Atom Feeds
Institute of Mathematical Statistics Lecture Notes - Monograph Series

Local polynomial regression on unknown manifolds

Peter J. Bickel, Bo Li

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.

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.

Primary Subjects: 62G08, 62H12
Secondary Subjects: 62G20
Keywords: local polynomial regression; manifolds

Full-text: Open access

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196794952
Digital Object Identifier: doi:10.1214/074921707000000148

back to Table of Contents

2008 © Institute of Mathematical Statistics

Institute of Mathematical Statistics Lecture Notes - Monograph Series

Institute of Mathematical Statistics Lecture Notes - Monograph Series