An information-theoretic alternative to maximum likelihood estimation method in ultrastructural measurement error model

Abstract

In this paper, a data constrained generalized maximum entropy (GME) estimator for the general linear measurement error model is proposed. GME estimation, as developed by (A. Golan, G. Judge and D. Miller A Maximum Entropy Econometrics: Robust Estimation with limited data (Wiley, New York, 1996)), was formulated as a convex mixed-integer nonlinear optimization problem. Shannon entropy measures and its generalization, namely ‘entropy of order r’ by Tsallis and R´enyi are briefly discussed. A Monte Carlo comparison is made with the classical maximum likelihood estimation (MLE) method. The results show that, with moderate sample size; the GME outperforms the MLE estimators in terms of mean squared error.