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Maximum Empirical Likelihood: Empty Set Problem

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  • Grendar, Marian
  • Judge, George G

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.

Suggested Citation

  • 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.
    • Handle: RePEc:cdl:agrebk:qt71v338mh
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    1. 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.
    2. Yijie Xue & Nicole Lazar, 2012. "Empirical likelihood-based hot deck imputation methods," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 629-646.
    3. Roberto Baragona & Francesco Battaglia & Domenico Cucina, 2017. "Empirical likelihood ratio in penalty form and the convex hull problem," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 507-529, November.
    4. Varron, Davit, 2016. "Empirical likelihood confidence tubes for functional parameters in plug-in estimation," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 100-118.
    5. Grendar, Marian & Judge, George G., 2010. "Revised empirical likelihood," CUDARE Working Papers 91799, University of California, Berkeley, Department of Agricultural and Resource Economics.

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