Analysis of variance, coefficient of determination and $F$-test for local polynomial regression

Simple item page
dc.creatorHuang, Li-Shan
dc.creatorChen, Jianwei
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:13:24Z
dc.date.available2026-07-07T10:13:24Z
dc.descriptionThis 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOS531 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0810.4808
dc.identifierhttp://arxiv.org/abs/0810.4808
dc.identifierAnnals of Statistics 2008, Vol. 36, No. 5, 2085-2109
dc.identifierdoi:10.1214/07-AOS531
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172520
dc.subjectStatistics Theory
dc.subject62G08 (Primary) 62J10 (Secondary)
dc.titleAnalysis of variance, coefficient of determination and $F$-test for local polynomial regression
dc.typetext

Files

Collections

arXiv