Novel calibrated inference strategies for multiplicative distortion beta models: theory, efficiency, and empirical applications

This study tackles estimation and hypothesis testing in a multiplicative distortion model with an unobserved Beta-distributed variable distorted by an observable confounder. We propose three calibrated estimators for model parameters: maximum likelihood, moment-based by utilizing expectation-variance and symmetric moment ratios, and log-moments estimators, and analyse their theoretical properties and asymptotic efficiency. We then investigate two hypothesis tests: one for parameter equality for symmetry and another for Beta distribution goodness-of-fit. For symmetry testing, three test statistics are introduced and their asymptotic properties under the null hypothesis are explored; for goodness-of-fit, a novel symmetric covariance measure and test statistic are proposed. Monte Carlo simulations compare our methods with existing approaches, and a real-world dataset analysis illustrates their practical utility.