Semiparametric estimation of nonlinear errors-in-variables models with validation study

Consider the nonlinear regression model Y = g{X,β0) + e, where the explanatory variable X or the response Y is erroneously measured. Specifically, let X and ydenote the imperfect variables for X and Y respectively. When only X, when only Y, and when both AT, and Y axe measured with error, the primary survey data set contains observations on (Y, X), (Y, X), and (Y, X), respectively. With a proper validation sample for each of the above cases, we first assess the relationship between variables observed in the primary data via a nonparametric regression using the validation data and then obtain estimators of the regression parameters based on the least squares criterion using the primary data. The proposed estimators are robust against the misspecification of the distribution of the measurement error. The resulting estimators are shown to be. consistent and asymptotically normally distributed with asymptotic covariances capturing the dispersion induced by the nonparametric estimation.