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Maximum Empirical Likelihood: Empty Set Problem

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  • Grendar, Marian
  • Judge, George G
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    Abstract

    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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    Keywords: statistical theory; statistics; mathematical analysis; mathematical statistics; statistical theory; statistics; mathematical analysis; mathematical statistics; Physical Sciences and Mathematics;

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    1. Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," NBER Technical Working Papers 0186, National Bureau of Economic Research, Inc.
    2. 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.
    3. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    4. Mittelhammer,Ron C. & Judge,George G. & Miller,Douglas J., 2000. "Econometric Foundations Pack with CD-ROM," Cambridge Books, Cambridge University Press, number 9780521623940.
    5. Florens, J.P. & Rolin, J.M., 1994. "Bayes, Bootsrap, Moments," Papers 94.336, Toulouse - GREMAQ.
    6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
    7. 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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    Cited by:
    1. Grendar, Marian & Judge, George G., 2010. "Revised empirical likelihood," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt6gs579r0, Department of Agricultural & Resource Economics, UC Berkeley.
    2. Grendar, Marian & Judge, George G., 2010. "Maximum Likelihood with Estimating Equations," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt1r45k876, Department of Agricultural & Resource Economics, UC Berkeley.

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