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Maximum likelihood with estimating equations

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  • Grendar, Marian
  • Judge, George G.

Abstract

Methods, like Maximum Empirical Likelihood (MEL), that operate within the Empirical Estimating Equations (E3) approach to estimation and inference are challenged by the Empty Set Problem (ESP). We propose to return from E3 back to the Estimating Equations, and to use the Maximum Likelihood method. In the discrete case the Maximum Likelihood with Estimating Equations (MLEE) method avoids ESP. In the continuous case, how to make ML-EE operational is an open question. Instead of it, we propose a Patched Empirical Likelihood, and demonstrate that it avoids ESP. The methods enjoy, in general, the same asymptotic properties as MEL.

Suggested Citation

  • Grendar, Marian & Judge, George G., 2010. "Maximum likelihood with estimating equations," CUDARE Working Papers 56691, University of California, Berkeley, Department of Agricultural and Resource Economics.
    • Handle: RePEc:ags:ucbecw:56691
    DOI: 10.22004/ag.econ.56691
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    References listed on IDEAS

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    1. Grendar, Marian & Judge, George G., 2009. "Maximum Empirical Likelihood: Empty Set Problem," CUDARE Working Papers 53402, University of California, Berkeley, Department of Agricultural and Resource Economics.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Bruce Brown & Song Chen, 1998. "Combined and Least Squares Empirical Likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(4), pages 697-714, December.
    4. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
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    6. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    7. Grendar, Marian & Judge, George G, 2009. "Maximum empirical likelihood : empty set problem," CUDARE Working Paper Series 1090, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
    8. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
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