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This article studies the estimation of correlation coefficient between unobserved variables of interest. These unobservable variables are distorted in both multiplicative and additive fashion by an observed confounding variable. We propose several estimators for the correlation coefficient. Some of estimators are shown to 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. An improved estimation method for no additive distortion scenario is also considered. 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.

Estimation of correlation coefficient with general distortion measurement errors