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We consider the parameter estimation for multiplicative linear regression models with or without multiplicative distortion measurement errors. For the latter, both the response variable and the covariates are are unobserved and distorted by unknown functions of a commonly observable confounding variable. With or without distortion measurement errors, we propose the general least product relative error estimator, and we discuss the estimation efficiency with the least squares estimators by taking logarithmic transformation. Asymptotic properties for the estimators are established. Simulation studies are conducted to demonstrate the performance of the proposed estimation procedures.

General least product relative error estimation for multiplicative regression models with or without multiplicative distortion measurement errors