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Large Deviations Theory and Empirical Estimator Choice

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  • Grendar, Marian
  • Judge, George G.

Abstract

Criterion choice is such a hard problem in information recovery and in estimation and inference. In the case of inverse problems with noise, can probabilistic laws provide a basis for empirical estimator choice? That is the problem we investigate in this paper. Large Deviations Theory is used to evaluate the choice of estimator in the case of two fundamental situations-problems in modelling data. The probabilistic laws developed demonstrate that each problem has a unique solution-empirical estimator. Whether other members of the empirical estimator family can be associated a particular problem and conditional limit theorem, is an open question.

Suggested Citation

  • Grendar, Marian & Judge, George G., 2006. "Large Deviations Theory and Empirical Estimator Choice," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt20n3j23r, Department of Agricultural & Resource Economics, UC Berkeley.
  • Handle: RePEc:cdl:agrebk:qt20n3j23r
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    References listed on IDEAS

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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. 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.
    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. Marian Grendar Jr & Marian Grendar, 2003. "Maximum Probability/Entropy translating of contiguous categorical observations into frequencies," Econometrics 0309003, EconWPA.
    5. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    6. 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.
    7. 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.
    8. Francesco Bravo, "undated". "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
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