Analysis of variance, coefficient of determination and \(F\)-test for local polynomial regression

DOI10.1214/07-AOS531zbMath1148.62055arXiv0810.4808MaRDI QIDQ955131

Li-Shan Huang, Jianwei Chen

Publication date: 18 November 2008

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.4808

zbMATH Keywords

bandwidthvarying coefficient modelssmoothing splinesmodel checkingnonparametric regressionprojection matrixR-squared

Mathematics Subject Classification ID

Nonparametric regression and quantile regression (62G08) Estimation in multivariate analysis (62H12) Analysis of variance and covariance (ANOVA) (62J10)

Related Items (19)

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Uses Software

• KernSmooth
• SemiPar

Cites Work

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• The existence and asymptotic properties of a backfitting projection algorithm under weak conditions
• Correlation curves: Measures of association as functions of covariate values
• Nonparametric \(F\)-tests for nested global and local polynomial models
• Statistical estimation in varying coefficient models
• Generalized likelihood ratio statistics and Wilks phenomenon
• Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression
• Smoothing methods in statistics
• On the use of nonparametric regression for model checking
• Weak and strong uniform consistency of kernel regression estimates
• Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data
• Correlation Curves as Local Measures of Variance Explained by Regression
• Semiparametric Regression
• Calibrating the Degrees of Freedom for Automatic Data Smoothing and Effective Curve Checking
• A jump-preserving curve fitting procedure based on local piecewise-linear kernel estimation
• Smooth Backfitting in Practice
• Neighborhood correlation
• A nonparametric least-squares test for checking a polynomial relationship

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