Linear regression models with general distortion measurement errors

Abstract

This article considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with both multiplicative and additive distortion measurement errors. We transform the linear regression models via the varying coefficient models, then moment-based estimators are proposed by using the estimated varying coefficient functions. We study the asymptotic results of the proposed estimator, and construct a test statistic to check whether the coefficient in the linear model is zero or not. Lastly, we make some comparisons between the proposed estimators and other existing estimators through the simulation.

Keywords:

• Multiplicative distortion measurement errors
• Additive distortion measurement errors
• Local linear smoothing
• Varying coefficient models

Mathematics Subject Classification (2000):

• 62G05;⋅62G08;⋅62G20

Acknowledgments

The authors thank the editor, the associate editor, and a referee for their constructive suggestions that helped us to improve the early manuscript.

Additional information

Funding

Jun Zhang’s research was supported by the National Natural Science Foundation of China (Grant No. 11871411).