Regressions with Berkson errors in covariates - A nonparametric approach

TL;DR

This paper introduces a nonparametric method using instrumental variables to identify and estimate regression models with Berkson measurement errors, demonstrating its effectiveness through simulations and real-world epidemiological data.

Contribution

It provides a novel nonparametric estimator for Berkson errors in regressors, establishing its consistency and practical applicability.

Findings

Berkson errors significantly impact nonlinear regression estimates.

The proposed estimator performs well in simulations.

Application to air pollution data shows the method's practical usefulness.

Abstract

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.