Posterior consistency of nonparametric conditional moment restricted models

Yuan Liao*, Wenxin Jiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g 0. 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) thintail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior with nonshrinking variance. In addition, g 0 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.

Original languageEnglish (US)
Pages (from-to)3003-3031
Number of pages29
JournalAnnals of Statistics
Issue number6
StatePublished - Dec 2011


  • Bayesian inference
  • Identified region
  • Ill-posed problem
  • Limited information likelihood
  • Nonparametric instrumental variable
  • Partial identification
  • Regularization
  • Shrinkage prior
  • Sieve approximation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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