arXiv 20 Aug 2026 · Statistics — Methodology
arXiv:2608.19634 · PDF · Extracted main text
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.
appendix boundary found by appendix_titled_section at “Supplementary Material” · 99% of the source is main text. Read the extracted text to check this.
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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Tanaka, M (2026) curvature-calibrated quasi-Bayesian updating for moment-restricted models self | 0.974 | 13 | 4 | 92% |
| 2 | Chernozhukov, V. & Hong, H (2003) An MCMC approach to classical estimation | 0.644 | 2 | 2 | 100% |
| 3 | Hansen, L. P., Heaton, J., & Yaron, A (1996) Finite-sample properties of some alternative GMM estimators | 0.644 | 2 | 2 | 100% |
| 4 | Miller, J. W (2021) Asymptotic normality, concentration, and coverage of generalized posteriors | 0.511 | 2 | 1 | 100% |
| 5 | Bissiri, P. G., Holmes, C. C., & Walker, S. G (2016) A general framework for updating belief distributions | 0.405 | 1 | 1 | 100% |
| 6 | Chib, S., Shin, M., & Simoni, A (2018) Bayesian estimation and comparison of moment condition models | 0.405 | 1 | 1 | 100% |
| 7 | Dawid, A. P (1982) The well-calibrated Bayesian | 0.405 | 1 | 1 | 100% |
| 8 | Del Moral, P., Doucet, A., & Jasra, A (2006) Sequential Monte Carlo samplers | 0.405 | 1 | 1 | 100% |
| 9 | Fitzmaurice, G. M. & Laird, N. M (1993) A likelihood-based method for analysing longitudinal binary responses | 0.405 | 1 | 1 | 100% |
| 10 | Frazier, D. T., Drovandi, C., & Kohn, R (2026) Calibrated generalized Bayesian inference | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 33 scored citations.