Generalized maximum entropy (GME) estimator: formulation and a monte carlo study

Eruygur, H. Ozan (2005): Generalized maximum entropy (GME) estimator: formulation and a monte carlo study.

Abstract

The origin of entropy dates back to 19th century. In 1948, the entropy concept as a measure of uncertainty was developed by Shannon. A decade after in 1957, Jaynes formulated Shannon’s entropy as a method for estimation and inference particularly for ill-posed problems by proposing the so called Maximum Entropy (ME) principle. More recently, Golan et al. (1996) developed the Generalized Maximum Entropy (GME) estimator and started a new discussion in econometrics. This paper is divided into two parts. The first part considers the formulation of this new technique (GME). Second, by Monte Carlo simulations the estimation results of GME will be discussed in the context of non-normal disturbances.

• Item Type: MPRA Paper
• Language: English
• Keywords: Entropy, Maximum Entropy, ME, Generalized Maximum Entropy, GME, Monte Carlo Experiment, Shannon’s Entropy, Non-normal disturbances
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Jaynes, E. T. (1957). "Information Theory and Statistical Mechanics." Physics Review, 106, 620-630.

Golan, A., Judge, G. and Miller D. (1996), Maximum Entropy Econometrics: Robust Estimation With Limited Data, John Wiley & Sons.

Kapur, J.N., & Kesavan, H.K. (1992), Entropy Optimization Principles with Applications, Academic Press, London.

Mittelhammer, R. and S. Cardell (1997), “On the Consistency and Asymptotic Normality of the Data Constrained GME Estimator of the GML”, Working Paper, Washington State University, Pullman, WA.

Mittelhammer R., G. Judge, and D. Miller (2000), Econometric Foundations, Cambridge University Press.

Mittelhammer, R., S. Cardell and L. Marsh T. (2002), “The Data Constrained GME Estimator of the GML: Asymptotic Theory and Inference”, Working Paper, Washington State University, Pullman, WA.

Pukelsheim. F. (1994). “The Three Sigma Rule”, American Statistician, 48, 88-91.