Additive distortion measurement errors regression models with exponential calibration

Abstract

In this paper, we used the newly proposed exponential calibration for the additive distortion measurement errors models, where neither the response variable nor the covariates can be directly observed but are distorted in additive fashions by an observed confounding variable. By using the exponential calibrated variables, three estimators of parameters and empirical likelihood-based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of model checking, an adaptive Neyman test statistic restricted is proposed. Simulation studies demonstrate the performance of the proposed estimators and the test statistic. A real example is analysed to illustrate its practical usage.

Keywords:

• Exponential calibration
• local linear smoothing
• additive distortion
• measurement errors

Mathematics Subject Classifications (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.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Xuehu Zhu's research was supported by the National Social Science Foundation of China [21BTJ048].