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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 - Comue de Toulouse - Communauté d'universités et établissements 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] - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - Groupe ENSAE-ENSAI - Groupe des Écoles Nationales d'Économie et Statistique - IP Paris - Institut Polytechnique de Paris - 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 ?.
(This abstract was borrowed from another version of this item.)

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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    Citations

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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. Christopher D. Walker, 2024. "Semiparametric Bayesian Inference for a Conditional Moment Equality Model," Papers 2410.16017, arXiv.org.
    5. 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.
    6. Isaiah Andrews & Anna Mikusheva, 2022. "Optimal Decision Rules for Weak GMM," Econometrica, Econometric Society, vol. 90(2), pages 715-748, March.
    7. Christoph Breunig & Ruixuan Liu & Zhengfei Yu, 2022. "Double Robust Bayesian Inference on Average Treatment Effects," Papers 2211.16298, arXiv.org, revised Feb 2025.
    8. 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 Apr 2025.

    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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