Correlation coefficient-based measure for checking symmetry or asymmetry of a continuous variable with additive distortion

Abstract

This paper studies how to estimate and test the symmetry of a continuous variable under the additive distortion measurement errors setting. The unobservable variable is distorted in a additive fashion by an observed confounding variable. In this paper, a direct plug-in estimation procedure and two-step direct plug-in estimation procedure for correlation coefficient are proposed to measure the symmetry or asymmetry of a continuous variable, and empirical likelihood based confidence intervals are constructed to test the symmetry of the unobserved variable. The asymptotic properties of the proposed estimators and test statistics are investigated. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators and test statistics. These methods are applied to analyze a real dataset for an illustration.

Keywords:

• Confounding variables
• Distortion measurement errors
• Correlation coefficient
• Empirical likelihood

Acknowledgments

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

Additional information

Funding

Yujie Gai’s research was supported Discipline Construction Funds of Central University of Finance and Economics, and supported by Program for Innovation Research in Central University of Finance and Economics (Grant No. 020250319007).