Regression models with multiplicative distortion measurement errors: a two-stage calibration approach

We delve into nonlinear regression models in the presence of multiplicative distortion measurement errors and introduce a two-stage calibration approach. The first stage employs a parametric calibration method, whereas the second stage adopts a fully nonparametric calibration technique, complemented by identifiability conditions for the distortion functions. Furthermore, we relax the stringent independence assumptions typically imposed in the literature on multiplicative distortion regression models. We investigate parameter estimation and hypothesis testing within the model framework, along with their corresponding asymptotic properties. To address the goodness-of-fit issue, we utilize a dimension reduction-based model checking method. Simulation studies showcase the efficacy of the proposed procedure detailed in this paper, and a real-world application is analyzed to demonstrate its practical utility.