A new logarithmic multiplicative distortion for correlation analysis

We study the Pearson correlation coefficient in a logarithmic manner under the presence of multiplicative distortion measurement errors. In this context, the observed variables with logarithmic transformation are distorted in multiplicative fashions by an observed confounding variable. The proposed multiplicative distortion model in this paper is applied to analyze positive variables. We utilize the conditional mean calibration and the conditional absolute mean calibration methods to obtain the calibrated variables. Furthermore, we propose confidence intervals based on asymptotic normality, empirical likelihood, and jackknife empirical likelihood. Simulation studies demonstrate the effectiveness of the proposed estimation procedure, and a real‐world example is analyzed to illustrate its practical application.