Analysis of variance, coefficient of determination and F-test for local polynomial regression
Li-Shan Huang and Jianwei Chen
Source: Ann. Statist. Volume 36, Number 5 (2008), 2085-2109.
Abstract
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.
Primary Subjects: 62G08
Secondary Subjects: 62J10
Keywords: Bandwidth; nonparametric regression; projection matrix; R-squared; smoothing splines; varying coefficient models; model checking
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1223908085
Digital Object Identifier: doi:10.1214/07-AOS531
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