The data-constrained generalized maximum entropy estimator of the GLM: asymptotic theory and inference
type: Item
instance of: scholarly article
title: The data-constrained generalized maximum entropy estimator of the GLM: asymptotic theory and inference
zbMATH Open document ID: 1296.62058
author: Ron C. Mittelhammer
author: Nicholas Scott Cardell
author: Thomas L. Marsh
published in: Entropy
publication date: 2014-09-19T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 6346139
zbMATH Keywords: generalized maximum entropy
zbMATH Keywords: generalized maximum cross-entropy
zbMATH Keywords: asymptotic theory
zbMATH Keywords: GME computation
zbMATH Keywords: unbiased GME
zbMATH Keywords: GME as Bayesian estimation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/e15051756
OpenAlex ID: W2041614974
cites work: Information Theoretic Approaches to Inference in Moment Condition Models
cites work: An Information-Theoretic Alternative to Generalized Method of Moments Estimation
cites work: Q3687500
cites work: On some entropy methods in data analysis
cites work: A Mathematical Theory of Communication
cites work: Q4365235
cites work: Maximum entropy estimation of density and regression functions
cites work: A Maximum Entropy Approach to Recovering Information From Multinomial Response Data
cites work: Maximum entropy Lorenz curves
cites work: Statistical equilibrium in one-step forward looking economic models
cites work: A maximum entropy approach to estimation and inference in dynamic models or Counting fish in the sea using maximum entropy
cites work: The maximum entropy approach in production frontier estimation
DOI: 10.3390/E15051756
description: scientific article; zbMATH DE number 6346139