Open Access
December 2004 Estimation of nonlinear models with Berkson measurement errors
Liqun Wang
Ann. Statist. 32(6): 2559-2579 (December 2004). DOI: 10.1214/009053604000000670


This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not necessarily normal. In addition, the distribution of the random error in the regression equation is nonparametric. A minimum distance estimator is proposed, which is based on the first two conditional moments of the response variable given the observed predictor variables. To overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals, a simulation-based estimator is constructed. Consistency and asymptotic normality for both estimators are derived under fairly general regularity conditions.


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Liqun Wang. "Estimation of nonlinear models with Berkson measurement errors." Ann. Statist. 32 (6) 2559 - 2579, December 2004.


Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1068.62072
MathSciNet: MR2153995
Digital Object Identifier: 10.1214/009053604000000670

Primary: 62F12 , 62J02
Secondary: 65C05 , 65C60

Keywords: asymptotic normality , consistency , errors-in-variables , method of moments , minimum distance estimator , Nonlinear regression , Semiparametric model , simulation-based estimator , weighted least squares

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 6 • December 2004
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