@article{7bc00d48520b48dbb34c59c54bbf95f4,
title = "The MM, ME, ML, EL, EF and GMM approaches to estimation: A synthesis",
abstract = "The approaches employed for the estimation of different statistical estimates were studied. The statistical estimations under study belonged to the class of method of moments (MM), maximum likelihood estimation (MLE), estimating function (EF), maximum entropy (ME), and generalized method of moments (GMM). The basic idea behind the testing approaches was to check wheather the assumed probability model adequately described the data at hand. The derivation of estimation techniques as a special case of power divergence criterion, obtained via Peason χ2 statistics, was analyzed.",
keywords = "Empirical likelihood, Entropy, Estimating function, Generalized method of moments, History of estimation, Karl Pearson's goodness-of-fit statistic, Likelihood, Method of moment, Power divergence criterion",
author = "Bera, {Anil K.} and Yannis Bilias",
note = "Funding Information: We are grateful to Amos Golan and two anonymous referees for many helpful suggestions that have considerably improved the paper. An earlier version of this paper under the title “A Brief History of Estimation” was presented at a conference in honor of George Judge held at the University of Illinois, May 1–2, 1999. We wish to acknowledge helpful comments from the participants, in particular, from George Judge and Arnold Zellner. Kostas Fokianos, Alastair Hall and Yuichi Kitamura kindly provided some extra references and/or detailed comments. We would also like to thank Tatyana Dubovyk for providing very competent research assistance and Naoko Miki for her help in preparing the manuscript. Special thanks are due to Amos Golan without whose encouragement and kind prodding the paper would not have been completed. However, we retain the responsibility for any remaining errors. Financial support from the Office of Research, College of Commerce and Business Administration, University of Illinois of Urbana-Champaign (for Anil Bera) and from University of Cyprus (for Yannis Bilias) is gratefully acknowledged. This paper is dedicated to George Judge for his lifelong and continuing contribution to econometrics.",
year = "2002",
month = mar,
doi = "10.1016/S0304-4076(01)00113-0",
language = "English (US)",
volume = "107",
pages = "51--86",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
number = "1-2",
}