NONPARAMETRIC REGRESSION WITH NONPARAMETRICALLY GENERATED COVARIATES

• 成果类型: Article
• 署名作者: Mammen, Enno; Rothe, Christoph; Schienle, Melanie
• 署名单位: University of Mannheim; Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics; Humboldt University of Berlin
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS995
• 发表日期: 2012
• 页码: 1132-1170
• 关键词: simultaneous-equations models; Semiparametric models; uniform consistency; series estimators; kernel estimation; CONVERGENCE; variance; rates

摘要

We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous applications, including two-stage nonparametric regression, estimation of simultaneous equation models or censored regression models. Yet so far there seems to be no general theory for their impact on the final estimator's statistical properties. Our paper provides such results. We derive a stochastic expansion that characterizes the influence of the generation step on the final estimator, and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates.