The Annals of Statistics

Bayesian analysis in moment inequality models

Yuan Liao and Wenxin Jiang

Full-text: Open access

Abstract

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information likelihood. The posterior distribution converges to zero exponentially fast on any δ-contraction outside the identified region. Inside, it is bounded below by a positive constant if the identified region is assumed to have a nonempty interior. Our simulation evidence indicates that the Bayesian approach has advantages over frequentist methods, in the sense that, with a proper choice of the prior, the posterior provides more information about the true parameter inside the identified region. We also address the problem of moment and model selection. Our optimality criterion is the maximum posterior procedure and we show that, asymptotically, it selects the true moment/model combination with the most moment inequalities and the simplest model.

Article information

Source
Ann. Statist., Volume 38, Number 1 (2010), 275-316.

Dates
First available in Project Euclid: 31 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1262271616

Digital Object Identifier
doi:10.1214/09-AOS714

Mathematical Reviews number (MathSciNet)
MR2589323

Zentralblatt MATH identifier
1181.62025

Subjects
Primary: 62F15: Bayesian inference 62N01: Censored data models
Secondary: 62F99: None of the above, but in this section

Keywords
Identified region limited information likelihood consistent set estimation maximum posterior model and moment selection

Citation

Liao, Yuan; Jiang, Wenxin. Bayesian analysis in moment inequality models. Ann. Statist. 38 (2010), no. 1, 275--316. doi:10.1214/09-AOS714. https://projecteuclid.org/euclid.aos/1262271616


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