Modal linear regression models with additive 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 additive distortion measurement errors. Two calibration procedures are used to estimate parameters in the modal linear regression models, namely, conditional mean calibration and conditional mean calibration with exponential transformation. The asymptotic properties for the estimators based on two 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 temperature forecast dataset for an illustration.