Average derivation estimation with multiplicative distortion measurement errors

We consider the average derivation estimation when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. Three calibration procedures with several estimation methods are used to estimate the average derivation, namely, conditional mean calibration, conditional absolute mean calibration and conditional variance calibration. The asymptotic properties for the estimators are established. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators.