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Entropy 2013, 15(5), 1756-1775; doi:10.3390/e15051756
Article

The Data-Constrained Generalized Maximum Entropy Estimator of the GLM: Asymptotic Theory and Inference

1,* , 2
 and 3
1 Economic Sciences and Statistics, Washington State University, Pullman, WA 99164, USA 2 Salford Systems, San Diego, CA 92126, USA 3 Economic Sciences and IMPACT Center, Washington State University, Pullman, WA 99164, USA
* Author to whom correspondence should be addressed.
Received: 7 April 2013 / Revised: 23 April 2013 / Accepted: 7 May 2013 / Published: 14 May 2013
Download PDF [297 KB, 24 February 2015; original version 24 February 2015]

Abstract

Maximum entropy methods of parameter estimation are appealing because they impose no additional structure on the data, other than that explicitly assumed by the analyst. In this paper we prove that the data constrained GME estimator of the general linear model is consistent and asymptotically normal. The approach we take in establishing the asymptotic properties concomitantly identifies a new computationally efficient method for calculating GME estimates. Formulae are developed to compute asymptotic variances and to perform Wald, likelihood ratio, and Lagrangian multiplier statistical tests on model parameters. Monte Carlo simulations are provided to assess the performance of the GME estimator in both large and small sample situations. Furthermore, we extend our results to maximum cross-entropy estimators and indicate a variant of the GME estimator that is unbiased. Finally, we discuss the relationship of GME estimators to Bayesian estimators, pointing out the conditions under which an unbiased GME estimator would be efficient.
Keywords: generalized maximum entropy; generalized maximum cross-entropy; asymptotic Theory; GME computation; unbiased GME; GME as Bayesian estimation generalized maximum entropy; generalized maximum cross-entropy; asymptotic Theory; GME computation; unbiased GME; GME as Bayesian estimation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Mittelhammer, R.; Cardell, N.S.; Marsh, T.L. The Data-Constrained Generalized Maximum Entropy Estimator of the GLM: Asymptotic Theory and Inference. Entropy 2013, 15, 1756-1775.

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