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Revised empirical likelihood

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  • Grendar, Marian
  • Judge, George G.

Abstract

Empirical Likelihood (EL) and other methods that operate within the Empirical Estimating Equations (E3) approach to estimation and inference are challenged by the Empty Set Problem (ESP). ESP concerns the possibility that a model set, which is data-dependent, may be empty for some data sets. To avoid ESP we return from E3 back to the Estimating Equations, and explore the Bayesian infinite-dimensional Maximum A-posteriori Probability (MAP) method. The Bayesian MAP with Dirichlet prior motivates a Revised EL (ReEL) method. ReEL i) avoids ESP as well as the convex hull restriction, ii) attains the same basic asymptotic properties as EL, and iii) its computation complexity is comparable to that of EL.

Suggested Citation

  • 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.
    • Handle: RePEc:cdl:agrebk:qt6gs579r0
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    References listed on IDEAS

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    1. Yuichi Kitamura, 2007. "Nonparametric Likelihood: Efficiency And Robustness," The Japanese Economic Review, Japanese Economic Association, vol. 58(1), pages 26-46, March.
    2. 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.
    3. Grendar, Marian & Judge, George G, 2009. "Maximum Empirical Likelihood: Empty Set Problem," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt71v338mh, Department of Agricultural & Resource Economics, UC Berkeley.
    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.
    5. 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.
    6. 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.
    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.
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    Cited by:

    1. Jaeger, Adam & Lazar, Nicole A., 2020. "Split sample empirical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

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