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arXiv · 2604.23176

Misspecification-Averse Estimation

Isaiah Andrews·Ricky Li·Yucheng Shang
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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.

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Isaiah Andrews, Ricky Li, Yucheng Shang. 2026-04-25. Misspecification-Averse Estimation. https://arxiv.org/abs/2604.23176

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