You've Got to be Efficient: Ambiguity, Misspecification and Variational Preferences

Abstract

We develop a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification, which involves uniformly expanding a frequentist ambiguity set by a Kullback-Leibler radius. Optimal decisions are equivalent to minimax decisions under an exponentially tilted loss: misspecification tilts the loss, while ambiguity selects the least favorable prior. This separation permits local asymptotic analysis under general misspecification, allowing for both local and global priors. For estimation and treatment-assignment, optimal decisions coincide with those under correct specification for any degree of misspecification, including in semiparametric models. This favors maximum-likelihood over simulated method of moments, and efficient GMM over diagonally weighted alternatives.