| Title:
|
Optimal sequential multiple hypothesis tests (English) |
| Author:
|
Novikov, Andrey |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
309-330 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
sequential analysis |
| Keyword:
|
hypothesis testing |
| Keyword:
|
multiple hypotheses |
| Keyword:
|
discrete-time stochastic process |
| Keyword:
|
dependent observations |
| Keyword:
|
optimal sequential test |
| Keyword:
|
Bayes sequential test |
| MSC:
|
60G40 |
| MSC:
|
62C10 |
| MSC:
|
62L10 |
| MSC:
|
62L15 |
| idMR:
|
MR2518154 |
| . |
| Date available:
|
2010-06-02T18:33:11Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140077 |
| . |
| Reference:
|
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| Reference:
|
[2] J. Cochlar: The optimum sequential test of a finite number of hypotheses for statistically dependent observations.Kybernetika 16 (1980), 36–47. Zbl 0434.62060, MR 0575415 |
| Reference:
|
[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 |
| Reference:
|
[4] T. S. Ferguson: Mathematical Statistics: A Decision Theoretic Approach.Academic Press, New York 1967. Zbl 0153.47602, MR 0215390 |
| Reference:
|
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| Reference:
|
[6] J. Kiefer and L. Weiss: Some properties of generalized sequential probability ratio tests.Ann. Math. Statist. 28 (1957), 57–75. MR 0087290 |
| Reference:
|
[7] E. L. Lehmann: Testing Statistical Hypotheses.Wiley, New York; Chapman & Hall, London 1959. Zbl 1076.62018, MR 0107933 |
| Reference:
|
[8] G. Lorden: Structure of sequential tests minimizing an expected sample size.Z. Wahrsch. Verw. Gebiete 51 (1980), 291–302. Zbl 0407.62055, MR 0566323 |
| Reference:
|
[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 |
| Reference:
|
[10] L. Weiss: On sequential tests which minimize the maximum expected sample size.J. Amer. Statist. Assoc. 57 (1962), 551–566. Zbl 0114.10304, MR 0145630 |
| Reference:
|
[11] Sh. Zacks: The Theory of Statistical Inference.Wiley, New York – London – Sydney – Toronto 1971. Zbl 0321.62003, MR 0420923 |
| . |
