Estimation for varying coefficient partially nonlinear models with distorted measurement errors

In this paper, we propose a new varying coefficient partially nonlinear model where both the response and predictors are not directly observed, but are observed by unknown distorting functions of a commonly observable covariate. Because of the complexity of the model, existing estimation methods cannot be directly employed. For this, we propose using an efficient nonparametric regression to estimate the unknown distortion functions concerning the covariates and response on the distorting variable, and further, we obtain the profile nonlinear least squares estimators for the parameters and the coefficient functions using the calibrated variables. Furthermore, we establish the asymptotic properties of the resulting estimators. To illustrate our proposed methodology, we carry out some simulated and real examples.