Bounded tilting estimation

The search for one-step alternatives to the generalized method of moment (GMM) has identified broad classes of potential estimators such as generalized empirical likelihoods (GEL), empirical cressie-read (ECR), exponentially tilted empirical likelihood (ETEL), and minimum discrepancy (MD) estimators. While empirical likelihood (EL) dominates other ECR estimators in terms of higher-order asymptotics, it lacks robustness to model misspecification. ETEL was shown to combine higher-order efficiency and robustness to misspecification but demands strong moment generating function existence conditions. We show, both theoretically and via simulations, how to achieve the same goal under weaker moment existence conditions within the class of MD estimators.