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