Bandwidth selection for smooth backfitting in additive models

Details Bandwidth selection for smooth backfitting in additive models Bandwidth selection for smooth backfitting in additive models

2005-07-21

arxiv.org/abs/math/0507425v1

Annals of Statistics 2005, Vol. 33, No. 3, 1260-1294

Mathematics

Statistics Theory

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

Scientific paper

10.1214/009053605000000101

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.

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