Open Access
June 2013 Regressions with Berkson errors in covariates—A nonparametric approach
Susanne M. Schennach
Ann. Statist. 41(3): 1642-1668 (June 2013). DOI: 10.1214/13-AOS1122


This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via Monte Carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health. These examples illustrate that Berkson errors can clearly not be neglected in nonlinear regression models and that the proposed method represents an effective remedy.


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Susanne M. Schennach. "Regressions with Berkson errors in covariates—A nonparametric approach." Ann. Statist. 41 (3) 1642 - 1668, June 2013.


Published: June 2013
First available in Project Euclid: 1 August 2013

zbMATH: 1292.62061
MathSciNet: MR3113824
Digital Object Identifier: 10.1214/13-AOS1122

Primary: 62G08
Secondary: 62H99

Keywords: Berkson measurement error , errors in variables , instrumental variables , nonparametric inference , Nonparametric maximum likelihood

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 3 • June 2013
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