Multiplicative distortion measurement errors linear models with general moment identifiability condition

ABSTRACT

This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. The distortion functions for this kind of measurement errors are modelled under a general identifiability condition. For parameter estimation, we propose two calibration procedures: the conditional mean calibration based least squares estimation and the varying coefficient based estimation. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed. Simulation studies are conducted to compare the proposed calibration procedures and a real example is analysed to illustrate its practical usage.

Keywords:

• Calibration
• confidence intervals
• local linear smoothing
• least squared estimator
• multiplicative distortion measurement errors

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.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jun Zhang http://orcid.org/0000-0003-4332-5182

Additional information

Funding

Wangli Xu's research was supported by National Natural Science Foundation of China (Grant No: 11971478), the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (Grant No: 16JJD910002), and fund for building world-class universities (disciplines) of Renmin University of China (Grant No. KYGJD2019003). Yujie Gai's research was supported by Program for Innovation Research in Central University of Finance and Economics.