Estimation and Inference in the Case of Competing Sets of Estimating Equations

When there is uncertainty concerning the appropriate statistical model and corresponding estimators and inference methods, we consider the use of the maximum empirical likelihood principle to define an estimator, beta overbar (alpha hat), that combines plausible estimation problems. This estimation procedure identifies an optimal empirical likelihood driven convex-combination of competing estimators for the unknown parameters associated with the alternative plausible structural model specifications of the data sampling processes. The optimization is handled internally and avoids the tuning parameters usually necessary in problems of this type. To illustrate finite sample performance, an extensive sampling experiment is conducted in the context of the general linear model to demonstrate the adaptive nature and robustness of the estimator for an array of data sampling specifications