New Perspectives on Statistical Decisions Under Ambiguity

This review summarizes and connects recent work on the foundations and applications of statistical decision theory. Minimax models of decisions making under ambiguity are identified as a thread running through several literatures. In axiomatic decision theory, these models motivated a large literature on modeling ambiguity aversion. Some findings of this literature are reported in a way that should be directly accessible to statisticians and econometricians. In statistical decision theory, the models inform a rich theory of estimation and treatment choice, which was recently extended to account for partial identification and thereby ambiguity that does not vanish with sample size. This literature is illustrated by discussing global, finite-sample admissible, and minimax decision rules for a number of stylized decision problems with point and partial identification.