Minimax Sequential Tests for Many Composite Hypotheses. II

B. E. Brodskii, B. S. Darhovsky

Central Economics and Mathematics Institute, RAS

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/tvp316

 English version: Theory of Probability and its Applications, 2009, 53:1, 1–12

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