Optimal sequential multiple hypothesis tests
Kybernetika, Tome 45 (2009) no. 2, pp. 309-330 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 60G40, 62C10, 62L10, 62L15
Keywords: sequential analysis; hypothesis testing; multiple hypotheses; discrete-time stochastic process; dependent observations; optimal sequential test; Bayes sequential test
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Novikov, Andrey. Optimal sequential multiple hypothesis tests. Kybernetika, Tome 45 (2009) no. 2, pp. 309-330. http://geodesic.mathdoc.fr/item/KYB_2009_45_2_a7/

[1] R. H. Berk: Locally most powerful sequential tests. Ann. Statist. 3 (1975), 373–381. | MR | Zbl

[2] J. Cochlar: The optimum sequential test of a finite number of hypotheses for statistically dependent observations. Kybernetika 16 (1980), 36–47. | MR | Zbl

[3] J. Cochlar and I. Vrana: On the optimum sequential test of two hypotheses for statistically dependent observations. Kybernetika 14 (1978), 57–69. | MR

[4] T. S. Ferguson: Mathematical Statistics: A Decision Theoretic Approach. Academic Press, New York 1967. | MR | Zbl

[5] M. Ghosh, N. Mukhopadhyay, and P. K. Sen: Sequential Estimation. Wiley, New York – Chichester – Weinheim – Brisbane – Singapore – Toronto 1997. | MR

[6] J. Kiefer and L. Weiss: Some properties of generalized sequential probability ratio tests. Ann. Math. Statist. 28 (1957), 57–75. | MR

[7] E. L. Lehmann: Testing Statistical Hypotheses. Wiley, New York; Chapman & Hall, London 1959. | MR | Zbl

[8] G. Lorden: Structure of sequential tests minimizing an expected sample size. Z. Wahrsch. Verw. Gebiete 51 (1980), 291–302. | MR | Zbl

[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

[10] L. Weiss: On sequential tests which minimize the maximum expected sample size. J. Amer. Statist. Assoc. 57 (1962), 551–566. | MR | Zbl

[11] Sh. Zacks: The Theory of Statistical Inference. Wiley, New York – London – Sydney – Toronto 1971. | MR | Zbl