Local polynomial regression on unknown manifolds
Peter J. Bickel, Bo Li
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
Institute of Mathematical Statistics Lecture Notes - Monograph Series