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We consider an errors-in-variables nonlinear structural model where the density of the response belongs to the exponential family. We estimate regression parameters and the dispersion parameter as well as parameters of the hidden variable. Following the modified quasi-likelihood method we construct a joint estimator that has the minimal asymptotic covariance matrix in a wide class of estimators. The polynomial and gamma models are studied in more detail.

An optimal joint estimator for regression parameters and the dispersion parameter in errors-in-variables nonlinear models