IJPAM: Volume 45, No. 2 (2008)
HYPOTHESES BASED ON INDEPENDENT OBSERVATIONS
Department of Mathematics
San Rafael Atlixco 186, col. Vicentina, C.P. 09340, Mexico D.F., MEXICO
Abstract.In this work, we consider a general problem of testing two simple hypotheses about the distribution of a discrete-time stochastic process with independent values. The structure of optimal sequential tests is characterized. As a criterion of optimization the average sample number under a third hypothesis is taken, which does not necessarily match one of the two hypotheses under consideration (a version of the modified Kiefer-Weiss problem).
In the particular case of independent and identically distributed observations, we describe the class of all sequential hypotheses tests which share the optimality property with the sequential probability ratio test (SPRT), as well as characterize the class of optimal sequential tests in the modified Kiefer-Weiss problem.
As an illustration of the general results, we characterize the
structure of the optimal sequential tests for processes with
independent values which are stationary beginning from some fixed
Received: April 11, 2008
AMS Subject Classification: 62L10, 62L15, 60G40
Key Words and Phrases: sequential analysis, sequential hypothesis testing, two simple hypotheses, discrete-time stochastic process, independent observations, optimal sequential test, sequential probability ratio test
Source: International Journal of Pure and Applied Mathematics