Bandwidth selection for smooth backfitting in additive models

• 成果类型: Article
• 署名作者: Mammen, E; Park, BU
• 署名单位: University of Mannheim; Seoul National University (SNU)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000101
• 发表日期: 2005
• 页码: 1260-1294
• 关键词: asymptotic properties; regression

摘要

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.