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This paper studies optimal decision rules, including estimators and tests, for weakly identified GMM models. We derive the limit experiment for weakly identified GMM, and propose a theoretically‐motivated class of priors which give rise to quasi‐Bayes decision rules as a limiting case. Together with results in the previous literature, this establishes desirable properties for the quasi‐Bayes approach regardless of model identification status, and we recommend quasi‐Bayes for settings where identification is a concern. We further propose weighted average power‐optimal identification‐robust frequentist tests and confidence sets, and prove a Bernstein‐von Mises‐type result for the quasi‐Bayes posterior under weak identification.
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Asymptotic consistency of loss‐calibrated variational Bayes
This paper establishes the asymptotic consistency of theloss‐calibrated variational Bayes(LCVB) method. LCVB is a method for approximately computing Bayesian posterior approximations in a “loss aware” manner. This methodology is also highly relevant in general data‐driven decision‐making contexts. Here, we establish the asymptotic consistency of both the loss‐ calibrated approximate posterior and the resulting decision rules. We also establish the asymptotic consistency of decision rules obtained from a “naive” two‐stage procedure that first computes a standard variational Bayes approximation and then uses this in the decision‐making procedure.
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- Award ID(s):
- 1812197
- PAR ID:
- 10453788
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Stat
- Volume:
- 9
- Issue:
- 1
- ISSN:
- 2049-1573
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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