Random Sets and Confidence Procedures

The set of confidence procedures is identified as a fundamental subset of the set of random sets. This is accomplished by defining a simple a-field on the codomain of a set-valued mapping such that the mapping is a confidence procedure if it is measurable relative to that a-field. The confidence procedure becomes Borei measurable when the a-field is generated by a topology that we also define. The resulting topology and a-fields are shown to be natural choices on &(R) — {0 }. The motivation for the approach is the same as that motivating the use of statistics in point estimation. The theory of confidence procedures in set estimation is shown to be a simple extension of the theory of statistics in point estimation.