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Gaussian processes and Bayesian moment estimation

Jean-Pierre Florens () and Anna Simoni
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Jean-Pierre Florens: Toulouse School of Economics

No 2015-09, Working Papers from Center for Research in Economics and Statistics

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 ?.

Keywords: Moment restrictions; Gaussian processes; overidenti?cation; posterior consistency; functional equation. (search for similar items in EconPapers)
JEL-codes: C11 C14 C13 (search for similar items in EconPapers)
Pages: 53
Date: 2015-11
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