Local polynomial regression on unknown manifolds

Details Local polynomial regression on unknown manifolds Local polynomial regression on unknown manifolds

2007-08-07

arxiv.org/abs/0708.0983v1

IMS Lecture Notes Monograph Series 2007, Vol. 54, 177-186

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921707000000148 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921707000000148

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.

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