On oracle property and asymptotic validity of Bayesian generalized method of moments

Cheng Li*, Wenxin Jiang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Statistical inference based on moment conditions and estimating equations is of substantial interest when it is difficult to specify a full probabilistic model. We propose a Bayesian flavored model selection framework based on (quasi-)posterior probabilities from the Bayesian Generalized Method of Moments (BGMM), which allows us to incorporate two important advantages of a Bayesian approach: the expressiveness of posterior distributions and the convenient computational method of Markov Chain Monte Carlo (MCMC). Theoretically we show that BGMM can achieve the posterior consistency for selecting the unknown true model, and that it possesses a Bayesian version of the oracle property, i.e. the posterior distribution for the parameter of interest is asymptotically normal and is as informative as if the true model were known. In addition, we show that the proposed quasi-posterior is valid to be interpreted as an approximate posterior distribution given a data summary. Our applications include modeling of correlated data, quantile regression, and graphical models based on partial correlations. We demonstrate the implementation of the BGMM model selection through numerical examples.

Original languageEnglish (US)
Pages (from-to)132-147
Number of pages16
JournalJournal of Multivariate Analysis
Volume145
DOIs
StatePublished - Mar 1 2016

Keywords

  • Bayesian
  • GEE (generalized estimating equations)
  • GMM (generalized method of moments)
  • MCMC
  • Model selection
  • Moment condition
  • Oracle property
  • Posterior validity

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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