A novel two-stage calibration framework for correlation estimation under multiplicative distortions

This study tackles the challenge of correlation estimation in the presence of multiplicative distortion measurement errors by introducing a novel two-stage calibration framework. The initial parametric pre-calibration stage utilizes parametric calibration techniques, which are subsequently enhanced through nonparametric kernel smoothing to accurately recover the distortion functions. This staged approach effectively alleviates bias amplification and overcomes inherent limitations of existing calibration methods, by preventing overcorrection artifacts and accommodating intricate relationships between observed and latent variables. For the estimation of correlation coefficient, we propose conditional mean calibration, varying-coefficient based estimators, and conditional absolute logarithmic calibration. We delve into the estimation procedures and their asymptotic properties, constructing confidence intervals with asymptotic normality and employing the empirical likelihood method within the model framework. Simulation studies and a real-world application illustrate the efficacy and practical utility of our proposed procedure.