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

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1 Author(s)
Schmitz, N. ; Inst. fur Math. Stat., WWU, Munster, Germany

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>

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Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 3 )