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Gaussian Processes and Bayesian Moment Estimation

Author

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  • 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 - 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
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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. 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.
    3. 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.
    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 Feb 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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