Title :
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
fDate :
5/1/1995 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
