Multiplicative distortion measurement errors linear models with general moment identifiability condition

This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. The distortion functions for this kind of measurement errors are modelled under a general identifiability condition. For parameter estimation, we propose two calibration procedures: the conditional mean calibration based least squares estimation and the varying coefficient based estimation. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed. Simulation studies are conducted to compare the proposed calibration procedures and a real example is analysed to illustrate its practical usage.