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Large-Deviations Theory and Empirical Estimator Choice

Author

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  • Marian Grendar
  • George Judge

Abstract

In this article, we consider the problem of criterion choice in information recovery and inference in a large-deviations (LD) context. Kitamura and Stutzer recognize that the Maximum Entropy Empirical Likelihood estimator can be given a LD justification (Kitamura and Stutzer, 2002). We demonstrate there exists a similar LD justification for Owen's Empirical Likelihood estimator (Owen, 2001). We tie the two empirical estimators and related LD theorems to two basic ill-posed inverse problems α and β. We note that other estimators in this family lack an LD footing and provide an extensive discussion of the implications of these results. The appendix contains formal statements regarding relevant LD theorems.

Suggested Citation

  • Marian Grendar & George Judge, 2008. "Large-Deviations Theory and Empirical Estimator Choice," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 513-525.
  • Handle: RePEc:taf:emetrv:v:27:y:2008:i:4-6:p:513-525
    DOI: 10.1080/07474930801960402
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