Random Sets and Confidence Procedures
نویسندگان
چکیده
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.
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تاریخ انتشار 2008