Realization of closed, convex, and symmetric subsets of the unit square as regions of risk for testing simple hypotheses

Realization of closed, convex, and symmetric subsets of the unit square as regions of risk for testing simple hypotheses

0.00 Avg rating0 Votes
Article ID: iaor19961859
Country: Germany
Volume: 42
Issue: 5
Start Page Number: 325
End Page Number: 329
Publication Date: Sep 1995
Journal: Metrika
Authors: ,
Abstract:

It is well-known that the region of risk for testing simple hypotheses is some closed, convex, and equ1-symmetric subset of the unit square, which contains the points (0, 0) and (1, 1). It is shown that for any such subset R of the unit square and any atomless probability measure P on some equ2-algebra there exists some probability measure Q on the same equ3-algebra such that R is the corresponding region of risk for testing P against Q. This generalizes an earlier result and is as a first step derived here for the special case, where P is equal to the uniform distribution on the unit interval. The corresponding distribution Q is given explicitly in this case and the general case is treated by some well-known measure-isomorphism. This method of proof shows that Q might be chosen to be of type equ4 for some equ5 satisfying equ6, where equ7 is a probability measure, which is absolutely continuous with respect to P and equ8 is a one-point mass.

Reviews

Required fields are marked *. Your email address will not be published.