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Large Deviations Theory and Empirical Estimator Choice

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  • Grendar, Marian
  • Judge, George G.
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    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.

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    Bibliographic Info

    Paper provided by Department of Agricultural & Resource Economics, UC Berkeley in its series Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series with number qt20n3j23r.

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    Date of creation: 01 Jan 2006
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    Handle: RePEc:cdl:agrebk:qt20n3j23r

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    Related research

    Keywords: entropy; information theory; large deviations; empirical likelihood; Boltzmann Jaynes Inverse Problem; probabilistic laws; Social and Behavioral Sciences;

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    1. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Guido W. Imbens & Phillip Johnson & Richard H. Spady, 1995. "Information Theoretic Approaches to Inference in Moment Condition Models," NBER Technical Working Papers 0186, National Bureau of Economic Research, Inc.
    3. 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.
    4. 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.
    5. Judge, George G. & Mittelhammer, Ronald C, 2003. "A semi-parametric basis for combining estimation problems under quadratic loss," CUDARE Working Paper Series 948, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
    6. Yuichi Kitamura, 2001. "Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions," Econometrica, Econometric Society, vol. 69(6), pages 1661-1672, November.
    7. Mittelhammer,Ron C. & Judge,George G. & Miller,Douglas J., 2000. "Econometric Foundations Pack with CD-ROM," Cambridge Books, Cambridge University Press, number 9780521623940.
    8. Francesco Bravo, . "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
    9. Marian Grendar Jr & Marian Grendar, 2003. "Maximum Probability/Entropy translating of contiguous categorical observations into frequencies," Econometrics 0309003, EconWPA.
    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.
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