Estimation of nonlinear models with Berkson measurement errors. (English) Zbl 1068.62072

Summary: This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors [J. Berkson, J. Am. Stat. Assoc. 45, 164–180 (1950; Zbl 0040.22404)]. 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.


62J02 General nonlinear regression
62F12 Asymptotic properties of parametric estimators
62G08 Nonparametric regression and quantile regression
65C60 Computational problems in statistics (MSC2010)
65C05 Monte Carlo methods
62G20 Asymptotic properties of nonparametric inference


Zbl 0040.22404


Full Text: DOI arXiv


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