Curvature-Calibrated Quasi-Bayesian Updating for Moment-Restricted Models
Abstract
Quadratic moment-based quasi-posteriors depend on a weighting matrix governing both the contributions of moment conditions and the scale of posterior uncertainty. We propose curvature-calibrated quasi-Bayesian (CCQB) updating, which iteratively evaluates the inverse of the estimated moment covariance (or long-run covariance) at the center of the resulting fixed-weight quasi-posterior. A two-part stopping rule monitors changes in the center and Monte Carlo error in estimating it. Under local regularity conditions, the ideal calibration map is contractive, and its fixed point is root-N consistent. The calibrated quasi-posterior and the sampling distribution of its center have the inverse Godambe information matrix as their root-N-scale covariance. Simulations show substantial gains over identity weighting. Further iteration has little effect in linear designs but improves calibration for some parameters in nonlinear settings, although nominal coverage is not uniformly achieved. An application to longitudinal childhood wheeze data illustrates the method under within-subject dependence.
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BibTeX
@misc{tanaka2026curvaturecalibrated,
title = {{Curvature-Calibrated Quasi-Bayesian Updating for Moment-Restricted Models}},
author = {Masahiro Tanaka},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.19634},
eprint = {2608.19634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19634},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Curvature-Calibrated Quasi-Bayesian Updating for Moment-Restricted Models
AU - Masahiro Tanaka
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2608.19634
UR - https://arxiv.org/abs/2608.19634
AB - Quadratic moment-based quasi-posteriors depend on a weighting matrix governing both the contributions of moment conditions and the scale of posterior uncertainty. We propose curvature-calibrated quasi-Bayesian (CCQB) updating, which iteratively evaluates the inverse of the estimated moment covariance (or long-run covariance) at the center of the resulting fixed-weight quasi-posterior. A two-part stopping rule monitors changes in the center and Monte Carlo error in estimating it. Under local regularity conditions, the ideal calibration map is contractive, and its fixed point is root-N consistent. The calibrated quasi-posterior and the sampling distribution of its center have the inverse Godambe information matrix as their root-N-scale covariance. Simulations show substantial gains over identity weighting. Further iteration has little effect in linear designs but improves calibration for some parameters in nonlinear settings, although nominal coverage is not uniformly achieved. An application to longitudinal childhood wheeze data illustrates the method under within-subject dependence.
ER -