Comparison of maximum entropy and higher-order entropy estimators

We show that generalized maximum entropy (GME) is the only estimation method that is consistent with a set of five axioms. The GME estimator can be nested using a single parameter, α, into two more general classes of estimators: GME-α estimators. Each of these GME-α estimators violates one of the five basic axioms. However, small-sample simulations demonstrate that certain members of these GME-α classes of estimators may outperform the GME estimation rule.