Point Decisions For Interval–Identified Parameters

This paper considers a decision maker who prefers to make a point decision when the object of interest is interval-identified with regular bounds. When the bounds are just identified along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an efficient lower bound estimator plus the half of the known interval length. However, when the interval length or any nontrivial upper bound for the length is not known, the minimax approach suffers from triviality because the maximal risk is associated with infinitely long identified intervals. In this case, this paper proposes a local asymptotic minimax regret approach and shows that the midpoint between semiparametrically efficient bound estimators is optimal.