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A note on the optimality ofk-stage tests

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Summary

This note deals with sequential tests requiring at mostk observations. First a lemma is proved concerning the form of Bayes solutions. Then it is demonstrated by giving a counter-example that the theorem ofWald andWolfowitz has no correspondence fork-stage tests.

Zusammenfassung

Es wird gezeigt, daß man beik-stufigen Tests zwar für die Gestalt vonBayes-Lösungen ein Analogon zu den unbeschränkten Sequenztests hat, daß aber der Satz vonWald undWolfowitz über die gleichmäßige Optimalität bzgl. des Stichprobenumfangs keine Entsprechung besitzt.

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References

  • Lehmann, E. L.: Testing Statistical Hypotheses. J. Wiley, New York 1959.

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  • Matthes, Th. K.: On the optimality of sequential probability ratio tests. Ann. Math. Stat.34, 1963, 18–21.

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  • Richter, H.: Optimale Sequenzwiederholungstests. Zeitschr. Wahrscheinlichkeitstheorie verw. Geb.5, 1966, 156–166.

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Authors and Affiliations

  1. Karlsruhe

    N. Schmitz

  2. Institut für Mathematische Statistik der Westfälischen Wilhelms-Universität, Roxelerstraße 64, 44, Münster

    N. Schmitz

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  1. N. Schmitz
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Schmitz, N. A note on the optimality ofk-stage tests. Metrika 19, 72–75 (1972). https://doi.org/10.1007/BF01893280

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  • DOI: https://doi.org/10.1007/BF01893280

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