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.
CITATION STYLE
Bickel, P. J., & Li, B. (2007). Local polynomial regression on unknown manifolds. In Complex Datasets and Inverse Problems (pp. 177–186). Institute of Mathematical Statistics. https://doi.org/10.1214/074921707000000148
Mendeley helps you to discover research relevant for your work.