Estimation of correlation coefficient with monotone transformation and multiplicative distortions

Jun Zhang, Xuan Yu, Siming Deng, JiongTao Zhong, Yisheng Zhou and Bingqing Lin

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 1, 1-33

Abstract: This article studies the estimation of the correlation coefficient between unobserved variables of interest. These unobservable variables, mixed with some known monotone link functions, are distorted in multiplicative fashion by an observed confounding variable. We propose four calibration methods for the unobserved variables and the estimation of the correlation coefficient. Theoretical results show that the proposed estimators of correlation coefficient can be asymptotically efficient as if there are no distortions in the variables. Moreover, we suggest an asymptotic normal approximation and an empirical likelihood-based statistic to construct the confidence intervals. We conduct Monte Carlo simulation experiments to examine the performance of the proposed estimators. These methods are applied to analyze a real dataset for an illustration.

Date: 2025
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DOI: 10.1080/03610926.2023.2288794

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