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Zbl 0899.62100
Tartakovsky, Alexander
(Tartakovskij, A.)
Asymptotically optimal sequential tests for nonhomogeneous processes. (English)
[J] Sequential Anal. 17, No.1, 33-61 (1998). ISSN 0747-4946; ISSN 1532-4176/e

Summary: It is shown that under certain conditions the matrix sequential probability ratio test (SPRT) and the combinations of ``rejecting'' SPRTs minimize all moments of the stopping time distribution in the problem of sequential testing of several simple hypotheses for nonhomogeneous processes when probabilities of errors tend to zero. We consider the general case of observation processes with discrete or continuous time parameter and asymmetric (relative to probabilities of errors) classes of tests.

MSC 2000:: *62L10 Sequential statistical analysis
62M02 Markov processes: hypothesis testing
60G40 Optimal stopping

Keywords: multi-alternative sequential tests; nonhomogeneous observations; one-sided SPRT; average excess; moment inequalities for martingales; asymptotic optimality; lower bounds for the moments of stopping time; matrix sequential probability ratio test

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