Advancing Coefficient of Variation Estimation Under Additive Distortion Measurement Errors: Exploring New Avenues Beyond Independence Assumptions

ABSTRACT This paper focuses on estimating the coefficient of variation for an unobservable variable within an additive distortion measurement errors framework, where the observed variable is a sum of the unobservable variable and an unknown contaminating function of a confounding variable. We use the conditional mean calibration approach to derive a calibrated variable and introduce the calibrated coefficient of variation. Asymptotic properties of the estimators are derived, showing their efficiency. Confidence intervals for the coefficient of variation are constructed using asymptotic normal‐based and empirical likelihood‐based methods. We also propose test statistics for examining the exponential distribution of the unobservable variable. To relax the independence assumption between the confounding and unobservable variables, two novel identifiability conditions are introduced. Simulation results and a real‐world dataset analysis validate the effectiveness and robustness of our approach.