Optimal Decision Rules Under Partial Identification

Understand

I consider a class of statistical decision problems in which the policymaker must decide between two policies to maximize social welfare (e.g., the population mean of an outcome) based on a finite sample.

• The framework introduced in this paper allows for various types of restrictions on the structural parameter (e.g., the smoothness of a conditional mean potential outcome function) and accommodates settings with partial identification of social welfare.
• As the main theoretical result, I derive a finite-sample optimal decision rule under the minimax regret criterion.
• This rule has a simple form, yet achieves optimality among all decision rules; no ad hoc restrictions are imposed on the class of decision rules.