Liao, Yuan and Jiang, Wenxin (2011): Posterior consistency of nonparametric conditional moment restricted models. Published in: Annals of Statistics , Vol. 39, No. 6 (2011): pp. 30033031.

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Abstract
This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinitedimensional parameter g0. We estimate it in a quasiBayesian 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) thintail 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.
Item Type:  MPRA Paper 

Original Title:  Posterior consistency of nonparametric conditional moment restricted models 
Language:  English 
Keywords:  Identified region; limited information likelihood; sieve approximation; nonparametric instrumental variable; illposed problem; partial identification; Bayesian inference; shrinkage prior; regularization 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C11  Bayesian Analysis: General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  38700 
Depositing User:  Yuan Liao 
Date Deposited:  10. May 2012 01:46 
Last Modified:  21. Feb 2013 07:37 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/38700 