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

This paper studies a semi-linear errors-in-variables model of the formYi=x'i[beta]+g(Ti)+ei,Xi=xi+ui(1[less-than-or-equals, slant]i[less-than-or-equals, slant]n). The estimators of parameters[beta],[sigma]2and 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 vector[beta]and the unknown parameter[sigma]2are strongly consistent and asymptotically normal. The estimator ofgalso achieves an optimal rate of convergence.