Geodesic
Minimax Sequential Tests for Many Composite Hypotheses.~II
Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 3-15

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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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     author = {B. E. Brodskii and B. S. Darhovsky},
     title = {Minimax {Sequential} {Tests} for {Many} {Composite} {Hypotheses.~II}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a0/}
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B. E. Brodskii; B. S. Darhovsky. Minimax Sequential Tests for Many Composite Hypotheses.~II. Teoriâ veroâtnostej i ee primeneniâ, Tome 53 (2008) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/TVP_2008_53_1_a0/