Nonparametric estimation of an additive model with a link function

• 成果类型: Article
• 署名作者: Horowitz, JL; Mammen, E
• 署名单位: Northwestern University; University of Mannheim
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000814
• 发表日期: 2004
• 页码: 2412-2443
• 关键词: asymptotic properties; regression; series

摘要

This paper describes an estimator of the additive components of a nonparametric additive model with a known link function. When the additive components are twice continuously differentiable, the estimator is asymptotically normally distributed with a rate of convergence in probability of n(-2/5). This is true regardless of the (finite) dimension of the explanatory variable. Thus, in contrast to the existing asymptotically normal estimator, the new estimator has no curse of dimensionality. Moreover, the estimator has an oracle property. The asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty.