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Asymptotic Efficiency of Three-Stage Hypothesis Tests

Gary Lorden
The Annals of Statistics
Vol. 11, No. 1 (Mar., 1983), pp. 129-140
Stable URL: http://www.jstor.org/stable/2240467
Page Count: 12
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Asymptotic Efficiency of Three-Stage Hypothesis Tests
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Abstract

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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