Local Polynomial Regression on Unknown Manifolds

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 predict...

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Bibliographic Details
Main Authors:	Bickel, Peter J., Li, Bo
Format:	Book Chapter
Language:	eng
Subjects:	Data smoothing Datasets Estimators Linear regression Mathematical functions Mathematical manifolds Mathematical vectors Oracles Polynomials
Online Access:	Get full text
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Summary:	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.
ISSN:	0749-2170 2328-3874