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On errors-in-variables in polynomial regression – Berkson case. (English) Zbl 0952.62062
Summary: A nonlinear Berkson model [see J. Berkson, J. Am. Stat. Assoc. 45, 164-180 (1950; Zbl 0040.22404)], particularly the polynomial Berkson model, is considered in this work. It is shown that without making any identifiability assumptions, all coefficient parameters in this model can be estimated consistently. In particular, the model is shown to be identifiable. However, unlike the linear Berkson model where one can estimate the coefficient parameters by ignoring the measurement error, in the polynomial Berkson model we must take into account the measurement error. An iterative reweighted least squares approach is taken to estimate the parameters in the model. The resulting estimates are found to be the solution of a set of estimating equations. Simulation results of the three methods discussed for large samples in a quadratic Berkson model are compared.

62J02 General nonlinear regression
62F10 Point estimation
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis