On Hong–Tamer’s estimator in nonlinear errors-in-variable regression models

Abstract

Under some regularity conditions, the paper provides an alternative proof for the revised moment conditions proposed by Hong and Tamer (2003) in the nonlinear least squares regression model, when the covariates are measured with Laplace error. The asymptotic normality of the revised moment estimates is developed. The choice of optimal weight functions is also discussed and a nearly optimal weight function is identified. Moreover, a simulation extrapolation estimation procedure is suggested when the estimating equations based on the revised moment conditions are difficult to solve. Simulation studies are conducted to evaluate the finite performance of the proposed methods.