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Comparison of maximum entropy and higher-order entropy estimators. (English) Zbl 1043.62001
Summary: 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, \(\alpha\), into two more general classes of estimators: GME-\(\alpha\) estimators. Each of these GME-\(\alpha\) estimators violates one of the five basic axioms. However, small-sample simulations demonstrate that certain members of these GME-\(\alpha\) classes of estimators may outperform the GME estimation rule.

MSC:
62B10 Statistical aspects of information-theoretic topics
62F10 Point estimation
62P20 Applications of statistics to economics
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