Correlation analysis with additive distortion measurement errors

ABSTRACT

This paper studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in a additive fashion by an observed confounding variable. Two estimators, a direct-plug-in estimator and a residual-based estimator, are proposed. Their asymptotical results are obtained, and the residual-based estimator is shown asymptotically efficient. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence interval. The empirical likelihood statistic is shown to be asymptotically chi-squared. Simulation studies are conducted to examine the performance of the proposed estimators. These methods are applied to analyse the Boston housing price data for an illustration.

KEYWORDS:

• Confounding variables
• errors-in-variables
• correlation coefficient
• empirical likelihood

Acknowledgements

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

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Zhang Jun's research is supported by the National Natural Sciences Foundation of China [Grant No.11401391], the Project of Department of Education of Guangdong Province of China [Grant No. 2014KTSCX112], and the Natural Science Foundation of Shenzhen University [Grant No. 701, 000360023408]. Chen Qian's research is supported by the Natural Science Foundation of Shenzhen University [Grant No. 701, 000360023408], and Zhou Nanguang's research is supported by the Natural Science Foundation of Shenzhen University [Grant No. 701, 000360023408].