Nonlinear and nonparametric regression and instrumental variables

• 成果类型: Article
• 署名作者: Carroll, RJ; Ruppert, D; Crainiceanu, CM; Tosteson, TD; Karagas, MR
• 署名单位: Texas A&M University System; Texas A&M University College Station; Cornell University; Johns Hopkins University; Dartmouth College
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000001088
• 发表日期: 2004
• 页码: 736-750
• 关键词: measurement error models; IN-VARIABLES; simulation-extrapolation; open questions; us population; cancer risk; splines; identification; distributions; Consistency

摘要

We consider regression when the predictor is measured with error and an instrumental variable (TV) is available. The regression function., or nonparametrically. Our major new result shows that the regression function and all parameters in can be modeled linearly, nonlinearly the measurement error model are identified under relatively weak conditions, much weaker than previously known to imply identifiability. In addition, we exploit a characterization of the IV estimator as a classical correction for attenuation method based on a particular estimate of the variance of the measurement error. This estimate of the measurement error variance allows us to construct functional nonparametric regression estimators making no assumptions about the distribution of the unobserved predictor and structural estimators that use parametric assumptions about this distribution. The functional estimators uses, simulation extrapolation or deconvolution kernels and the structural method uses Bayesian Markov chain Monte Carlo. The Bayesian estimator is found to significantly outperform the functional approach.