Asymptotic normality of parametric part in partially linear models with measurement error in the nonparametric part

We consider the partially linear model relating a response Y to predictors (X,T) with mean function XT Ø + g(T) when the T's are measured with additive error. We derive an estimator of Ø by modification local-likelihood method. The resulting estimator of Ø is shown to be asymptotically normal.We consider the partially linear model relating a response Y to predictors (X,T) with mean function XT Ø + g(T) when the T's are measured with additive error. We derive an estimator of Ø by modification local-likelihood method. The resulting estimator of Ø is shown to be asymptotically normal.