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Maximum Empirical Likelihood: Empty Set Problem

  • Grendar, Marian
  • Judge, George G
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    In the Empirical Estimating Equations (E^3) approach to estimation and inference estimating equations are replaced by their data-dependent empirical counterparts. It is odd but with E^3 there are models where the E^3-based estimator does not exist for some data set, and does exist for others. This depends on whether or not a set of data-supported probability mass functions that satisfy the empirical estimating equations is empty for the data set. In a finite sample context, this unnoted feature invalidates methods of estimation and inference, such as the Maximum Empirical Likelihood, that operate within E^3. The empty set problem of E^3 is illustrated by several examples and possible remedies are discussed.

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    Paper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt71v338mh.

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    Date of creation: 10 Sep 2009
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    Handle: RePEc:cdl:agrebk:qt71v338mh
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    1. 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.
    2. Florens, J.P. & Rolin, J.M., 1994. "Bayes, Bootsrap, Moments," Papers 94.336, Toulouse - GREMAQ.
    3. 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.
    4. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
    6. Bruce Brown & Song Chen, 1998. "Combined and Least Squares Empirical Likelihood," Annals of the Institute of Statistical Mathematics, Springer, vol. 50(4), pages 697-714, December.
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