Statistics Papers

Document Type

Journal Article

Date of this Version

1973

Publication Source

The Annals of Statistics

Volume

1

Issue

5

Start Page

902

Last Page

912

DOI

10.1214/aos/1176342510

Abstract

Let f : X × Y R. We prove two theorems concerning the existence of a measurable function φ such that f (x,φ(x)) = infy f(x,y). The first concerns Borel measurability and the second concerns absolute (or universal) measurability. These results are related to the existence of measurable projections of sets S X × Y. Among other applications these theorems can be applied to the problem of finding measurable Bayes procedures according to the usual procedure of minimizing the a posteriori risk. This application is described here and a counterexample is given in which a Borel measurable Bayes procedure fails to exist.

Comments

At the time of publication, author Lawrence Brown was affiliated with Cornell University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

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Date Posted: 27 November 2017

This document has been peer reviewed.