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Posterior consistency of nonparametric conditional moment restricted models

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  • Liao, Yuan
  • Jiang, Wenxin

Abstract

This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g0. We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior with nonshrinking variance. In addition, g0 is allowed to be only partially identified in the frequentist sense, and the parameter space does not need to be compact. The posterior is regularized using a slowly growing sieve dimension, and it is shown that the posterior converges to any small neighborhood of the identified region. We then apply our results to the nonparametric instrumental regression model. Finally, the posterior consistency using a random sieve dimension parameter is studied.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 38700.

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Date of creation: 2011
Date of revision:
Publication status: Published in Annals of Statistics 6.39(2011): pp. 3003-3031
Handle: RePEc:pra:mprapa:38700

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Related research

Keywords: Identified region; limited information likelihood; sieve approximation; nonparametric instrumental variable; ill-posed problem; partial identification; Bayesian inference; shrinkage prior; regularization;

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References

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Citations

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Cited by:
  1. Anna Simoni & Jean-Pierre Florens, 2013. "Regularizing Priors for Linear Inverse Problems," THEMA Working Papers 2013-32, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  2. Liao, Yuan & Jiang, Wenxin, 2011. "Posterior consistency of nonparametric conditional moment restricted models," MPRA Paper 38700, University Library of Munich, Germany.
  3. Jean-Pierre Florens & Anna Simoni, 2013. "Regularizing Priors for Linear Inverse Problems," Working Papers hal-00873180, HAL.
  4. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
  5. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
  6. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2014.

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