Local linear estimation for covariate-adjusted varying-coefficient models

We consider local linear estimation of varying-coefficient models in which the data are observed with multiplicative distortion which depends on an observed confounding variable. At first, each distortion function is estimated by non parametrically regressing the absolute value of contaminated variable on the confounder. Secondly, the coefficient functions are estimated by the local least square method on the basis of the predictors of latent variables, which are obtained in terms of the estimated distorting functions. We also establish the asymptotic normality of our proposed estimators and discuss the inference about the distortion function. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and a real dataset of Pima Indians diabetes is analyzed for illustration.