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Activity Number: 252
Type: Contributed
Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #307697
Title: Infinite Order Cross-Validated Local Polynomial Regression
Author(s): Jeffrey Racine*+ and Peter Gavin Hall
Companies: McMaster University and University of Melbourne
Keywords: Kernel ; Model Selection ; Adaptive
Abstract:

Many practical problems require nonparametric estimates of regression functions, and local polynomial regression has emerged as a leading approach. In applied settings practitioners often adopt either the local constant or local linear variants, or choose the order of the local polynomial to be slightly greater than the order of the maximum derivative estimate required. But such ad hoc determination of the polynomial order may not be optimal in general, while the joint determination of the polynomial order and bandwidth presents some interesting theoretical and practical challenges. In this paper we propose a data-driven approach towards the joint determination of the polynomial order and bandwidth, provide theoretical underpinnings, and demonstrate that improvements in both finite-sample efficiency and rates of convergence can thereby be obtained. In the case where the true data generating process (DGP) is in fact a polynomial whose order does not depend on the sample size, our method is capable of attaining the root-n rate often associated with correctly specified parametric models.


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