Open Access
October 2008 Analysis of variance, coefficient of determination and F-test for local polynomial regression
Li-Shan Huang, Jianwei Chen
Ann. Statist. 36(5): 2085-2109 (October 2008). DOI: 10.1214/07-AOS531


This paper provides ANOVA inference for nonparametric local polynomial regression (LPR) in analogy with ANOVA tools for the classical linear regression model. A surprisingly simple and exact local ANOVA decomposition is established, and a local R-squared quantity is defined to measure the proportion of local variation explained by fitting LPR. A global ANOVA decomposition is obtained by integrating local counterparts, and a global R-squared and a symmetric projection matrix are defined. We show that the proposed projection matrix is asymptotically idempotent and asymptotically orthogonal to its complement, naturally leading to an F-test for testing for no effect. A by-product result is that the asymptotic bias of the “projected” response based on local linear regression is of quartic order of the bandwidth. Numerical results illustrate the behaviors of the proposed R-squared and F-test. The ANOVA methodology is also extended to varying coefficient models.


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Li-Shan Huang. Jianwei Chen. "Analysis of variance, coefficient of determination and F-test for local polynomial regression." Ann. Statist. 36 (5) 2085 - 2109, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1148.62055
MathSciNet: MR2458180
Digital Object Identifier: 10.1214/07-AOS531

Primary: 62G08
Secondary: 62J10

Keywords: bandwidth , model checking , Nonparametric regression , projection matrix , R-squared , smoothing splines , varying coefficient models

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.36 • No. 5 • October 2008
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