Estimation of nonlinear models with Berkson measurement errors

The Annals of Statistics · 2004 · Volume 32 · Issue 6

Abstract

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.

Keywords

62F12, 62J02, 65C05, 65C60, asymptotic normality, consistency, errors-in-variables, method of moments, minimum distance estimator, Nonlinear regression, Semiparametric model, simulation-based estimator, weighted least squares

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