The Annals of Statistics

Estimation of nonlinear models with Berkson measurement errors

Liqun Wang

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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.

Article information

Ann. Statist., Volume 32, Number 6 (2004), 2559-2579.

First available in Project Euclid: 7 February 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J02: General nonlinear regression 62F12: Asymptotic properties of estimators
Secondary: 65C60: Computational problems in statistics 65C05: Monte Carlo methods

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


Wang, Liqun. Estimation of nonlinear models with Berkson measurement errors. Ann. Statist. 32 (2004), no. 6, 2559--2579. doi:10.1214/009053604000000670.

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