MINIMAX SEQUENTIAL TESTS FOR MANY COMPOSITE HYPOTHESES. II

摘要

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.