Misspecification-Averse Estimation

2026-04-25

AI Summary

This study addresses the problem of optimal estimation under potential misspecification of the likelihood function. Drawing on decision theory under uncertainty, it introduces an axiomatic class of constrained multiplier criteria that flexibly encode robust attitudes toward model misspecification. By extending classical efficiency bounds to a locally asymptotic limit experiment framework that accommodates moment condition misspecification, the paper establishes that the asymptotically optimal estimator coincides with the Bayesian decision rule derived from an exponentially tilted likelihood under a flat prior. The resulting plug-in estimator retains asymptotic optimality even when the model is misspecified, thereby achieving a marked improvement in both robustness and statistical efficiency.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• misspecification
• optimal estimation
• likelihood
• asymptotic minimax
• moment constraints

Innovation

• misspecification-averse estimation
• constrained multiplier criterion
• local asymptotic minimax
• exponentially tilted likelihood
• moment constraints