Multi-stage hypothesis tests are studied as competitors of sequential tests. A class of three-stage tests for the one-dimensional exponential family is shown to be asymptotically efficient, whereas two-stage tests are not. Moreover, in order to be asymptotically optimal, three-stage tests must mimic the behavior of sequential tests. Similar results are obtained for the problem of testing two simple hypotheses.
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G. Lorden (1983) studied this question.