NONPARAMETRIC COVARIATE-ADJUSTED REGRESSION

• 成果类型: Article
• 署名作者: Delaigle, Aurore; Hall, Peter; Zhou, Wen-Xin
• 署名单位: University of Melbourne; University of Melbourne; Princeton University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1442
• 发表日期: 2016
• 页码: 2190-2220
• 关键词: varying coefficient models; errors-in-variables; CONVERGENCE; disease; rates

摘要

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that relies on restrictive assumptions usually made in the literature, to a sophisticated piecewise approach that involves reconstructing a smooth curve from an estimator of a constant multiple of its absolute value, and which can be applied in much more general scenarios. We show that, although our nonparametric estimators are constructed from predictors of the unobserved undistorted data, they have the same first-order asymptotic properties as the standard estimators that could be computed if the undistorted data were available. We illustrate the good numerical performance of our methods on both simulated and real datasets.