A Fully Automated Bandwidth Selection Method for Fitting Additive Models

Abstract

This article describes a fully automated bandwidth selection method for additive models that is applicable to the widely used backfitting algorithm of Buja, Hastie, and Tibshirani. The proposed plug-in estimator is an extension of the univariate local linear regression estimator of Ruppert, Sheather, and Wand and is shown to achieve the same O_p (n ^–2/7) relative convergence rate for bivariate additive models. If more than two covariates are present, theoretical justification of the method requires independence of the covariates, but simulation experiments show that in practice the method is very robust to violations of this assumption. The proposed bandwidth selection method is compared to cross-validation through simulation experiments. Its practical behavior is demonstrated on a real dataset.

Key Words:

• Additive model
• Automatic bandwidth selection
• Housing prices
• Local polynomial regression
• Variance estimation.