Point Decisions for Interval-Identied Parameters

This paper considers a decision-maker who prefers to make a point decision when the object of interest is interval-identi…ed with regular bounds. When the bounds are just identi…ed along with known interval length, the local asymptotic minimax decision with respect to a symmetric convex loss function takes an obvious form: an e¢ cient 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 su¤ers from triviality because the maximal risk is associated with in…nitely long identi…ed intervals. In this case, this paper proposes a local asymptotic minimax regret approach and shows that the midpoint between semiparametrically e¢ cient bound estimators is optimal. Key words and Phrases: Interval Identi…cation, Semiparametric E¢ ciency, Local Asymptotic Minimax Regret Decisions. JEL Classi…cations: C01, C13, C14, C44.