Local polynomial regression on unknown manifolds
Statistics Theory
2009-09-29 v1 Statistics Theory
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.
Cite
@article{arxiv.0708.0983,
title = {Local polynomial regression on unknown manifolds},
author = {Peter J. Bickel and Bo Li},
journal= {arXiv preprint arXiv:0708.0983},
year = {2009}
}
Comments
Published at http://dx.doi.org/10.1214/074921707000000148 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)