Comment on "Optimality of the sequential probability ratio test for nonstationary observations" by Y. Liu and S.D. Blostein

Author

Schmitz, Norbert

Author_Institution

Inst. fur Math. Stat., WWU, Munster, Germany

Volume

41

Issue

3

fYear

1995

fDate

5/1/1995 12:00:00 AM

Firstpage

861

Abstract

For original paper see IEEE Trans. Inform. Theory, vol.38, p.177-82 (1992). Liu and Blostein (1992) consider sequential tests with varying stopping bounds (NSPRT) for testing simple hypotheses on independent but nonstationary observations. They state a considerable generalization of the famous Wald-Wolfowitz theorem [1948] on the (simultaneous) minimization of the expected sample sizes for given error probabilities (Liu and Blostein, Theorem 27). Unfortunately, this statement fails to be true: 1) a simple counterexample may be constructed by choosing densities f/sub 01//spl ne/f/sub 1,1/ such that 0>

Keywords

Bayes methods; error statistics; minimisation; probability; signal processing; Bayes-test; Wald-Wolfowitz theorem; a priori probabilities; costs; densities; error probabilities; losses; minimization; nonstationary observations; optimality; sample sizes; sequential probability ratio test; sequential tests; stopping bounds; Bismuth; Costs; Error correction codes; Error probability; Polynomials; Sequential analysis; Testing;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.382044

Filename

382044