Misspecification-Averse Estimation
Abstract
We study optimal estimation when the likelihood may be misspecified. Building on tools from the theory of decision-making under uncertainty, we analyze a class of axiomatically grounded optimality criteria which nests several existing misspecification-robust objectives. Within this class, we introduce the constrained multiplier criterion, which allows for flexible misspecification attitudes. We prove a local asymptotic minimax theorem for this criterion, extending a classical efficiency bound to a limit experiment which incorporates moment-constrained misspecification concerns. We characterize asymptotically optimal estimators as Bayes decision rules under a flat prior and an exponentially tilted likelihood that incorporates the moment constraints, and show that feasible plug-in analogs are asymptotically optimal.
Keywords
Cite
@article{arxiv.2604.23176,
title = {Misspecification-Averse Estimation},
author = {Isaiah Andrews and Ricky Li and Yucheng Shang},
journal= {arXiv preprint arXiv:2604.23176},
year = {2026}
}