POINT DECISIONS FOR INTERVAL–IDENTIFIED PARAMETERS
研究当参数被区间识别时，决策者如何做出点决策。对于已知区间长度的情况，给出了局部渐近极小极大决策的显式形式；当区间长度未知时，提出局部渐近极小极大遗憾方法，并证明区间中点估计是最优的。
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.