IDEAS home Printed from https://ideas.repec.org/p/ags/ucbecw/25084.html

Large Deviations Theory and Empirical Estimator Choice

Author

Listed:
  • 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," CUDARE Working Papers 25084, University of California, Berkeley, Department of Agricultural and Resource Economics.
    • Handle: RePEc:ags:ucbecw:25084
    DOI: 10.22004/ag.econ.25084
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/25084/files/wp061012.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.22004/ag.econ.25084?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Imbens, G., 1993. "A New Approach to Generalized Method on Moments Estimation," Harvard Institute of Economic Research Working Papers 1633, Harvard - Institute of Economic Research.
    2. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    3. 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.
    4. 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.
    5. 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.
    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. Francesco Bravo, "undated". "Bartlett-type Adjustments for Empirical Discrepancy Test Statistics," Discussion Papers 04/14, Department of Economics, University of York.
    10. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giuseppe Ragusa, 2011. "Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 406-456, August.
    2. Otsu, Taisuke, 2010. "On Bahadur efficiency of empirical likelihood," Journal of Econometrics, Elsevier, vol. 157(2), pages 248-256, August.
    3. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2013. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Econometrica, Econometric Society, vol. 81(3), pages 1185-1201, May.
    4. Prosper Dovonon, 2016. "Large Sample Properties of the Three-Step Euclidean Likelihood Estimators under Model Misspecification," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 465-514, April.
    5. Alain Guay & Jean-Francois Lamarche, 2005. "The Information Content of Implied Probabilities to Detect Structural Change," Working Papers 0804, Brock University, Department of Economics, revised Oct 2008.
    6. Susanne M. Schennach, 2014. "Entropic Latent Variable Integration via Simulation," Econometrica, Econometric Society, vol. 82(1), pages 345-385, January.
    7. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    8. Shane M. Sherlund, 2004. "Quasi Empirical Likelihood Estimation of Moment Condition Models," Econometric Society 2004 North American Summer Meetings 507, Econometric Society.
    9. Lô, Serigne N. & Ronchetti, Elvezio, 2012. "Robust small sample accurate inference in moment condition models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3182-3197.
    10. Caner, Mehmet, 2008. "Nearly-singular design in GMM and generalized empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 144(2), pages 511-523, June.
    11. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    12. Canay, Ivan A. & Otsu, Taisuke, 2012. "Hodges–Lehmann optimality for testing moment conditions," Journal of Econometrics, Elsevier, vol. 171(1), pages 45-53.
    13. Hongtu Zhu & Haibo Zhou & Jiahua Chen & Yimei Li & Jeffrey Lieberman & Martin Styner, 2009. "Adjusted Exponentially Tilted Likelihood with Applications to Brain Morphology," Biometrics, The International Biometric Society, vol. 65(3), pages 919-927, September.
    14. Richard Smith, 2005. "Weak instruments and empirical likelihood: a discussion of the papers by DWK Andrews and JH Stock and Y Kitamura," CeMMAP working papers CWP13/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. A. Felipe & N. Martín & P. Miranda & L. Pardo, 2018. "Testing with Exponentially Tilted Empirical Likelihood," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1319-1358, December.
    16. Alain Guay & Florian Pelgrin, 2007. "Using Implied Probabilities to Improve Estimation with Unconditional Moment Restrictions," Cahiers de recherche 0747, CIRPEE.
    17. Almeida, Caio & Garcia, René, 2012. "Assessing misspecified asset pricing models with empirical likelihood estimators," Journal of Econometrics, Elsevier, vol. 170(2), pages 519-537.
    18. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    19. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    20. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    21. Philip Kostov, 2013. "Empirical likelihood estimation of the spatial quantile regression," Journal of Geographical Systems, Springer, vol. 15(1), pages 51-69, January.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ags:ucbecw:25084. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/dabrkus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.