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Minimax Sequential Tests for Many Composite Hypotheses. I
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 4, pp. 625-643 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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B. E. Brodskii; B. S. Darhovsky. Minimax Sequential Tests for Many Composite Hypotheses. I. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 4, pp. 625-643. http://geodesic.mathdoc.fr/item/TVP_2007_52_4_a0/

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