Translator Disclaimer
VOL. 54 | 2007 Local polynomial regression on unknown manifolds

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.

Information

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

Digital Object Identifier: 10.1214/074921707000000148

Subjects:
Primary: 62G08, 62H12
Secondary: 62G20

Rights: Copyright © 2007, Institute of Mathematical Statistics

CHAPTER
10 PAGES


SHARE
Back to Top