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Keywords:
sequential analysis; hypothesis testing; multiple hypotheses; discrete-time stochastic process; dependent observations; optimal sequential test; Bayes sequential test
sequential analysis; hypothesis testing; multiple hypotheses; discrete-time stochastic process; dependent observations; optimal sequential test; Bayes sequential test
Summary:
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.
References:
[1] R. H. Berk: Locally most powerful sequential tests. Ann. Statist. 3 (1975), 373–381. MR 0368346 | Zbl 0332.62063
[2] J. Cochlar: The optimum sequential test of a finite number of hypotheses for statistically dependent observations. Kybernetika 16 (1980), 36–47. MR 0575415 | Zbl 0434.62060
[3] J. Cochlar and I. Vrana: On the optimum sequential test of two hypotheses for statistically dependent observations. Kybernetika 14 (1978), 57–69. MR 0488544
[4] T. S. Ferguson: Mathematical Statistics: A Decision Theoretic Approach. Academic Press, New York 1967. MR 0215390 | Zbl 0153.47602
[5] M. Ghosh, N. Mukhopadhyay, and P. K. Sen: Sequential Estimation. Wiley, New York – Chichester – Weinheim – Brisbane – Singapore – Toronto 1997. MR 1434065
[6] J. Kiefer and L. Weiss: Some properties of generalized sequential probability ratio tests. Ann. Math. Statist. 28 (1957), 57–75. MR 0087290
[7] E. L. Lehmann: Testing Statistical Hypotheses. Wiley, New York; Chapman & Hall, London 1959. MR 0107933 | Zbl 1076.62018
[8] G. Lorden: Structure of sequential tests minimizing an expected sample size. Z. Wahrsch. Verw. Gebiete 51 (1980), 291–302. MR 0566323 | Zbl 0407.62055
[9] A. Novikov: Optimal sequential tests for two simple hypotheses based on independent observations. Internat. J. Pure Appl. Math. 45 (2008), 2, 291–314. MR 2421867
[10] L. Weiss: On sequential tests which minimize the maximum expected sample size. J. Amer. Statist. Assoc. 57 (1962), 551–566. MR 0145630 | Zbl 0114.10304
[11] Sh. Zacks: The Theory of Statistical Inference. Wiley, New York – London – Sydney – Toronto 1971. MR 0420923 | Zbl 0321.62003
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