Set coverage and robust policy

Abstract: When conducting inference on partially identified parameters, confidence regions may cover the whole identified set with a prescribed probability, to which we will refer as set coverage, or they may cover each of its point with a prescribed probability, to which we will refer as point coverage. Since set coverage implies point coverage, confidence regions satisfying point coverage are generally preferred on the grounds that they may be more informative. The object of this note is to describe a decision problem in which, contrary to received wisdom, point coverage is clearly undesirable.