This article is cited in 4 papers

Minimax Sequential Tests for Many Composite Hypotheses. I

B. E. Brodskii^a, B. S. Darhovsky<sup>b

a</sup> Central Economics and Mathematics Institute, RAS
^b Institute of Systems Analysis, Russian Academy of Sciences

Abstract: The problem of sequential testing of many composite hypotheses is considered. Each hypothesis is described by the density function of observations that depends on a parameter from one of disjoint sets. New performance measures for one-sided and multisided sequential tests are proposed and nonasymptotical a priori lower bounds for these measures are proved. Sequential tests are found which use a minimax procedure on parametric sets for sequential likelihood ratio and are asymptotically optimal: the a priori lower bounds for performance measures are attained for these tests. All proofs are in Part II.

Keywords: composite multihypothesis testing, sequential tests.

Received: 26.06.2006

DOI: 10.4213/tvp1526

 English version: Theory of Probability and its Applications, 2008, 52:4, 565–579

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