期刊
ANNALS OF STATISTICS
卷 33, 期 3, 页码 1260-1294出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/009053605000000101
关键词
backtitting; bandwidth selection; penalized least squares; plug-in rules; nonparametric regression; Nadaraya-Watson; local polynomial smoothing
The smooth backfitting introduced by Marnmen, 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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