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Large-Deviations Theory and Empirical Estimator Choice

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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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    1. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    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. 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.
    4. Judge, George G. & Mittelhammer, Ron C, 2003. "A Semi-Parametric Basis for Combining Estimation Problems Under Quadratic Loss," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt8z25j0w3, Department of Agricultural & Resource Economics, UC Berkeley.
    5. Mittelhammer, Ron C & Judge, George G. & Schoenberg, Ron, 2003. "Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt2xm0n02g, Department of Agricultural & Resource Economics, UC Berkeley.
    6. Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
    7. Marian Grendar Jr & Marian Grendar, 2003. "Maximum Probability/Entropy translating of contiguous categorical observations into frequencies," Econometrics 0309003, University Library of Munich, Germany.
    8. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    9. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    10. Kitamura, Yuichi & Stutzer, Michael, 2002. "Connections between entropic and linear projections in asset pricing estimation," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 159-174, March.
    11. Francesco Bravo, "undated". "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
    12. Mittelhammer, Ron C & Judge, George G. & Schoenberg, Ron, 2003. "Empirical Evidence Concerning the Finite Sample Performance of EL-Type Structural Equation Estimation and Inference Methods," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt2xm0n02g, Department of Agricultural & Resource Economics, UC Berkeley.
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