Modal linear regression models with multiplicative distortion measurement errors

We consider modal linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. Four calibration procedures are used to estimate parameters in the modal linear regression models, namely, conditional mean calibration, conditional absolute mean calibration, conditional variance calibration, and conditional absolute logarithmic calibration. The asymptotic properties for the estimators based on four calibration procedures are established. Monte Carlo simulation experiments are conducted to examine the performance of the proposed estimators. The proposed estimators are applied to analyze a forest fires dataset for an illustration.