Semi-parametric estimation of Pearson correlation coefficient under additive distortion measurement errors

In this article, we investigate the estimation of the Pearson correlation coefficient in the present of additive distortion measurement errors, which are influenced by a shared, observed confounding variable. We introduce two estimators for the Pearson correlation coefficient: the profile least squares estimator and the moment-based estimator. Notably, these estimators do not rely on the assumption of independence between the confounding variable and the underlying variables. Furthermore, we demonstrate that the proposed estimators are asymptotically efficient. To evaluate their performance, we conduct comparisons between our proposed estimators and existing methods found in the literature through simulation studies. Additionally, we apply these methodologies to analyze a real dataset as an illustrative example.