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

Abstract

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.

Keywords:

• Distortion measurement errors
• Least product relative error estimation
• Local linear smoothing

Mathematics Subject Classification (2000):

• 62G05
• 62G08
• 62G20

Acknowledgements

The authors thank the editor, the associate editor, and a referee for their constructive suggestions that helped us to improve the early manuscript. Huili Zhou (ID: 2017222012) is a junior student majoring in Statistics at Shenzhen University, and this work was done when the first author was supervised by the corresponding author.