Set coverage and robust policy

TL;DR

This paper discusses confidence regions for partially identified parameters, highlighting a decision problem where point coverage is less desirable than set coverage, challenging common assumptions in statistical inference.

Contribution

It introduces a decision framework showing that, contrary to common belief, point coverage can be undesirable in certain inference scenarios.

Findings

Point coverage may be less informative than set coverage.

Confidence regions can be designed to favor set coverage in specific decision problems.

Challenging the assumption that point coverage is always preferable.

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.