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The Data-Constrained Generalized Maximum Entropy Estimator of the GLM: Asymptotic Theory and Inference
Economic Sciences and Statistics, Washington State University, Pullman, WA 99164, USA
Salford Systems, San Diego, CA 92126, USA
Economic Sciences and IMPACT Center, Washington State University, Pullman, WA 99164, USA
* Author to whom correspondence should be addressed.
Received: 7 April 2013; in revised form: 23 April 2013 / Accepted: 7 May 2013 / Published: 14 May 2013
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
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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.
Mittelhammer R, Cardell NS, Marsh TL. The Data-Constrained Generalized Maximum Entropy Estimator of the GLM: Asymptotic Theory and Inference. Entropy. 2013; 15(5):1756-1775.
Mittelhammer, Ron; Cardell, Nicholas S.; Marsh, Thomas L. 2013. "The Data-Constrained Generalized Maximum Entropy Estimator of the GLM: Asymptotic Theory and Inference." Entropy 15, no. 5: 1756-1775.