On Parameter Estimation for Semi-linear Errors-in-Variables Models

This paper studies a semi-linear errors-in-variables model of the formYi=x′iβ+g(Ti)+ei,Xi=xi+ui(1⩽i⩽n). The estimators of parametersβ,σ2and of the smooth functiongare derived by using the nearest neighbor-generalized least square method. Under some weak conditions, it is shown that the estimators of unknown vectorβand the unknown parameterσ2are strongly consistent and asymptotically normal. The estimator ofgalso achieves an optimal rate of convergence.