Additive distortion measurement errors regression models with exponential calibration

In this paper, we used the newly proposed exponential calibration for the additive distortion measurement errors models, where neither the response variable nor the covariates can be directly observed but are distorted in additive fashions by an observed confounding variable. By using the exponential calibrated variables, three estimators of parameters and empirical likelihood-based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of model checking, an adaptive Neyman test statistic restricted is proposed. Simulation studies demonstrate the performance of the proposed estimators and the test statistic. A real example is analysed to illustrate its practical usage.