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

Entropy

Ron Mittelhammer¹  Nicholas Scott Cardell² 

[1] Economic Sciences and Statistics, Washington State University, Pullman, WA 99164, USA;Salford Systems, San Diego, CA 92126, USA; E-Mail:

关键词: generalized maximum entropy;    generalized maximum cross-entropy;    asymptotic Theory;    GME computation;    unbiasedGME;    GME as Bayesian estimation;   

DOI  :  10.3390/e15051756

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.