The Annals of Statistics

Regressions with Berkson errors in covariates—A nonparametric approach

Susanne M. Schennach

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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.

Article information

Ann. Statist., Volume 41, Number 3 (2013), 1642-1668.

First available in Project Euclid: 1 August 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62H99: None of the above, but in this section

Berkson measurement error errors in variables instrumental variables nonparametric inference nonparametric maximum likelihood


Schennach, Susanne M. Regressions with Berkson errors in covariates—A nonparametric approach. Ann. Statist. 41 (2013), no. 3, 1642--1668. doi:10.1214/13-AOS1122.

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Supplemental materials

  • Supplementary material: Supplementary material to “Regressions with Berkson errors in covariates—A nonparametric approach”. The supplementary material provides (i) a proof of consistency of the proposed estimator, (ii) additional simulation results and (iii) various extensions of the method, including the weakening of some of full independence assumptions to conditional independence and handling the simultaneous presence of classical and Berkson errors.