Abstract
Three-stage $t$-tests of separated one-sided hypotheses are derived, extending Lorden's optimal three-stage tests for the one-dimensional exponential family by using Lai and Zhang's generalization of Schwarz's optimal fully-sequential tests to the multiparameter exponential family. The resulting three-stage $t$-tests are shown to be asymptotically optimal, achieving the same average sample size as optimal fully-sequential tests.
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