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Misspecification-Averse Estimation

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  • Isaiah Andrews
  • Ricky Li
  • Yucheng Shang

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.

Suggested Citation

  • Isaiah Andrews & Ricky Li & Yucheng Shang, 2026. "Misspecification-Averse Estimation," Papers 2604.23176, arXiv.org.
    • Handle: RePEc:arx:papers:2604.23176
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    File URL: http://arxiv.org/pdf/2604.23176
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