Nonparametric regression penalizing deviations from additivity

• 成果类型: Article
• 署名作者: Studer, M; Seifert, B; Gasser, T
• 署名单位: University of Zurich
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000001246
• 发表日期: 2005
• 页码: 1295-1329
• 关键词: local polynomial regression; estimators; models; CONVERGENCE; density; rates; weak

摘要

Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions imposed can lead to serious bias. Here, a new estimator is proposed which allows penalizing the nonadditive part of a regression function. This offers a smooth choice between the full and the additive model. As a byproduct, this penalty leads to a regularization in sparse regions. If the additive model does not hold, a small penalty introduces an additional bias compared to the full model which is compensated by the reduced bias due to using smaller bandwidths. For increasing penalties, this estimator converges to the additive smooth backfitting estimator of Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443-1490]. The structure of the estimator is investigated and two algorithms are provided. A proposal for selection of tuning parameters is made and the respective properties are studied. Finally, a finite sample evaluation is performed for simulated and ozone data.