The MM, ME, ML, EL, EF and GMM approaches to estimation: A synthesis

Anil K. Bera, Yannis Bilias

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)51-86
Number of pages36
JournalJournal of Econometrics
Issue number1-2
StatePublished - Mar 2002


  • 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

ASJC Scopus subject areas

  • Economics and Econometrics


Dive into the research topics of 'The MM, ME, ML, EL, EF and GMM approaches to estimation: A synthesis'. Together they form a unique fingerprint.

Cite this