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Curvature-Calibrated Quasi-Bayesian Updating for Moment-Restricted Models

Masahiro Tanaka

arXiv 20 Aug 2026 · Statistics — Methodology

arXiv:2608.19634 · PDF · Extracted main text

Abstract

Moment restrictions provide a flexible basis for quasi-Bayesian inference when a full likelihood is unavailable, but the weighting matrix in a quadratic moment criterion determines both the relative importance of the moments and the information scale of posterior updating. We propose curvature-calibrated quasi-Bayesian updating, which uses the inverse of the covariance (or long-run covariance) of the moment conditions evaluated at a self-consistent quasi-posterior center. The resulting fixed-point procedure alternates between covariance estimation and simulation from a fixed-weight quasi-posterior, thereby avoiding parameter-dependent weighting during each simulation run. Under a Bernstein-von Mises condition for the fixed-weight quasi-posterior at the efficient population weight, we show that the calibration map is locally contractive, that its fixed point is consistent at the standard parametric rate, and that the Gaussian approximation continues to hold under the calibrated data-dependent weight, with covariance given by the inverse Godambe information matrix. Under a uniform fourth-moment condition, the scaled quasi-posterior covariance converges to the same matrix, so quasi-posterior and repeated-sampling uncertainty agree to first order. Simulations show improved covariance calibration and interval coverage after a few updates. An application to longitudinal binary-response data illustrates the method with within-subject dependence and overidentified residual moments.

Citation extraction

33
references
48
in-text mentions
33
distinct cited
4
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10,232
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Tanaka, M (2026) curvature-calibrated quasi-Bayesian updating for moment-restricted models self0.97413492%
2Chernozhukov, V. & Hong, H (2003) An MCMC approach to classical estimation0.64422100%
3Hansen, L. P., Heaton, J., & Yaron, A (1996) Finite-sample properties of some alternative GMM estimators0.64422100%
4Miller, J. W (2021) Asymptotic normality, concentration, and coverage of generalized posteriors0.51121100%
5Bissiri, P. G., Holmes, C. C., & Walker, S. G (2016) A general framework for updating belief distributions0.40511100%
6Chib, S., Shin, M., & Simoni, A (2018) Bayesian estimation and comparison of moment condition models0.40511100%
7Dawid, A. P (1982) The well-calibrated Bayesian0.40511100%
8Del Moral, P., Doucet, A., & Jasra, A (2006) Sequential Monte Carlo samplers0.40511100%
9Fitzmaurice, G. M. & Laird, N. M (1993) A likelihood-based method for analysing longitudinal binary responses0.40511100%
10Frazier, D. T., Drovandi, C., & Kohn, R (2026) Calibrated generalized Bayesian inference0.40511100%

Showing the top 10 of 33 scored citations.