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December 2011 Posterior consistency of nonparametric conditional moment restricted models
Yuan Liao, Wenxin Jiang
Ann. Statist. 39(6): 3003-3031 (December 2011). DOI: 10.1214/11-AOS930

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.

Citation

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Yuan Liao. Wenxin Jiang. "Posterior consistency of nonparametric conditional moment restricted models." Ann. Statist. 39 (6) 3003 - 3031, December 2011. https://doi.org/10.1214/11-AOS930

Information

Published: December 2011
First available in Project Euclid: 24 January 2012

zbMATH: 1246.62087
MathSciNet: MR3012399
Digital Object Identifier: 10.1214/11-AOS930

Subjects:
Primary: 62F15 , 62G08 , 62G20
Secondary: 62P20

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

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 6 • December 2011
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