Optimal sequential multiple hypothesis tests

Andrey Novikov

Kybernetika (2009)

  • Volume: 45, Issue: 2, page 309-330
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Novikov, Andrey. "Optimal sequential multiple hypothesis tests." Kybernetika 45.2 (2009): 309-330. <http://eudml.org/doc/37735>.

@article{Novikov2009,
abstract = {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.},
author = {Novikov, Andrey},
journal = {Kybernetika},
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},
language = {eng},
number = {2},
pages = {309-330},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Optimal sequential multiple hypothesis tests},
url = {http://eudml.org/doc/37735},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Novikov, Andrey
TI - Optimal sequential multiple hypothesis tests
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 2
SP - 309
EP - 330
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/37735
ER -

References

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  1. Locally most powerful sequential tests, Ann. Statist. 3 (1975), 373–381. Zbl0332.62063MR0368346
  2. The optimum sequential test of a finite number of hypotheses for statistically dependent observations, Kybernetika 16 (1980), 36–47. Zbl0434.62060MR0575415
  3. On the optimum sequential test of two hypotheses for statistically dependent observations, Kybernetika 14 (1978), 57–69. MR0488544
  4. Mathematical Statistics: A Decision Theoretic Approach, Academic Press, New York 1967. Zbl0153.47602MR0215390
  5. Sequential Estimation, Wiley, New York – Chichester – Weinheim – Brisbane – Singapore – Toronto 1997. MR1434065
  6. Some properties of generalized sequential probability ratio tests, Ann. Math. Statist. 28 (1957), 57–75. MR0087290
  7. Testing Statistical Hypotheses, Wiley, New York; Chapman & Hall, London 1959. Zbl1076.62018MR0107933
  8. Structure of sequential tests minimizing an expected sample size, Z. Wahrsch. Verw. Gebiete 51 (1980), 291–302. Zbl0407.62055MR0566323
  9. Optimal sequential tests for two simple hypotheses based on independent observations, Internat. J. Pure Appl. Math. 45 (2008), 2, 291–314. MR2421867
  10. On sequential tests which minimize the maximum expected sample size, J. Amer. Statist. Assoc. 57 (1962), 551–566. Zbl0114.10304MR0145630
  11. The Theory of Statistical Inference, Wiley, New York – London – Sydney – Toronto 1971. Zbl0321.62003MR0420923

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