Power gain by pre-testing?

W. Albers, P.C. Boon, W.C.M. Kallenberg

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    Abstract

    The aim of this paper is to study whether it is possible to gain power by pretesting,
    and to give insight in when this occurs, to what extent and at which
    price. A pre-test procedure consists of a preliminary test which tests a particular
    property of a given restricted model, followed by a main test for the main
    hypothesis regarding the parameter of interest. After acceptance by the preliminary
    test, a basic main test is used in the restricted model. After rejection by
    the preliminary test, a more general main test is used which does not use prior
    information about the underlying distribution. The procedure is analyzed in the
    model against which the preliminary test protects. For classes of tests including
    the standard rst-order optimal tests, a transparent expression is given for the
    power and size dierence of the pre-test procedure compared to the power and
    (correct) size of the second main test. This expression is based on second-order
    asymptotics and gives qualitative and quantitative insight in the behavior of the
    procedure. It shows that substantial power gain, not merely due to size violation,
    is possible if the second main test really diers from the basic main test. The
    smaller the correlation between the two main tests, the larger the power gain.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages22
    Publication statusPublished - 1999

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1488
    ISSN (Print)0169-2690

    Keywords

    • MSC-62E20
    • MSC-62F05
    • Pre-test procedure
    • Power gain
    • Robustness of validity
    • Second-order asymtotics

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    • Power gain by pre-testing?

      Albers, W., Boon, P. C. & Kallenberg, W. C. M., 2001, In: Statistics and decisions. 19, 3, p. 253-276 24 p.

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