Bandwidth selection for smooth backfitting in additive models

Abstract

The smooth backfitting introduced by Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443-1490] is a promising technique to fit additive regression models and is known to achieve the oracle efficiency bound. In this paper, we propose and discuss three fully automated bandwidth selection methods for smooth backfitting in additive models. The first one is a penalized least squares approach which is based on higher-order stochastic expansions for the residual sums of squares of the smooth backfitting estimates. The other two are plug-in bandwidth selectors which rely on approximations of the average squared errors and whose utility is restricted to local linear fitting. The large sample properties of these bandwidth selection methods are given. Their finite sample properties are also compared through simulation experiments.

Published at http://dx.doi.org/10.1214/009053605000000101 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (10)

• Fast stable direct fitting and smoothness selection for Generalized Additive Models
• Estimation of a semiparametric transformation model
• Smooth backfitting in generalized additive models
• Exploring spatial nonlinearity using additive approximation
• Rate-optimal estimation for a general class of nonparametric regression models with unknown link functions
• Flexible generalized varying coefficient regression models
• A simple smooth backfitting method for additive models
• Semi-parametric regression: Efficiency gains from modeling the nonparametric part
• Projection-type estimation for varying coefficient regression models
• Asymptotics for in-sample density forecasting