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Gaussian Processes and Bayesian Moment Estimation

Author

Listed:
  • Jean-Pierre Florens

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Anna Simoni

    (CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

Abstract

Given a set of moment restrictions that characterize a parameter ?, we investigate a semiparametric Bayesian approach for estimation of ? that imposes these moment restrictions in the nonparametric prior for the data distribution. As main contribution, we construct a degenerate Gaussian process prior for the density function associated with the data distribution F that imposes overidentifying restrictions. We show that this prior is computationally convenient. Since the likelihood function is not speci?ed by the model we construct it based on a linear functional transformation of F that has an asymptotically Gaussian empirical counterpart. This likelihood is used to construct the posterior distribution. We provide a frequentist validation of our procedure by showing: consistency of the maximum a posteriori estimator for ?, consistency and asymptotic normality of the posterior distribution of ?.
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Suggested Citation

  • Jean-Pierre Florens & Anna Simoni, 2019. "Gaussian Processes and Bayesian Moment Estimation," Post-Print hal-02903252, HAL.
    • Handle: RePEc:hal:journl:hal-02903252
    DOI: 10.1080/07350015.2019.1668799
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    References listed on IDEAS

    as
    1. Florens, Jean-Pierre & Simoni, Anna, 2016. "Regularizing Priors For Linear Inverse Problems," Econometric Theory, Cambridge University Press, vol. 32(1), pages 71-121, February.
    2. 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.
    3. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    4. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    5. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, September.
    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. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    8. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, September.
    9. 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.
    10. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
    11. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, September.
    12. Jean-Pierre Florens & Anna Simoni, 2012. "Regularized Posteriors in Linear Ill-Posed Inverse Problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 214-235, June.
    13. Kim, Jae-Young, 2002. "Limited information likelihood and Bayesian analysis," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 175-193, March.
    14. Susanne M. Schennach, 2005. "Bayesian exponentially tilted empirical likelihood," Biometrika, Biometrika Trust, vol. 92(1), pages 31-46, March.
    15. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    16. Giuseppe Ragusa, 2007. "Bayesian Likelihoods for Moment Condition Models," Working Papers 060714, University of California-Irvine, Department of Economics.
    17. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, September.
    18. Susanne M. Schennach, 2007. "Point estimation with exponentially tilted empirical likelihood," Papers 0708.1874, arXiv.org.
    19. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
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    Cited by:

    1. Siddhartha Chib & Minchul Shin & Anna Simoni, 2022. "Bayesian estimation and comparison of conditional moment models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 740-764, July.
    2. Gallant, A. Ronald & Hong, Han & Leung, Michael P. & Li, Jessie, 2022. "Constrained estimation using penalization and MCMC," Journal of Econometrics, Elsevier, vol. 228(1), pages 85-106.
    3. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    4. Dante Amengual & Enrique Sentana, 2016. "Comments on: Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 248-252.
    5. Isaiah Andrews & Anna Mikusheva, 2022. "Optimal Decision Rules for Weak GMM," Econometrica, Econometric Society, vol. 90(2), pages 715-748, March.
    6. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2022. "Double Robust Bayesian Inference on Average Treatment Effects," Papers 2211.16298, arXiv.org, revised Oct 2024.
    7. Christopher D. Walker, 2023. "Parametrization, Prior Independence, and the Semiparametric Bernstein-von Mises Theorem for the Partially Linear Model," Papers 2306.03816, arXiv.org, revised Feb 2024.

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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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