Data driven rank tests for classes of tail alternatives

Willem/Wim Albers, W.C.M. Kallenberg, F. Martini

    Research output: Book/ReportReportOther research output

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    Abstract

    Tail alternatives describe the frequent occurrence of a non-constant shift in the two-sample problem with a shift function increasing in the tail. The classes of shift functions can be built up using Legendre polynomials. It is important to rightly choose the number of polynomials involved. Here this choice is based on the data, using a modification of Schwarz's selection rule. Given the data driven choice of the model, appropriate rank tests are applied. Simulations show that the new data driven rank tests work very well. While other tests for detecting shift alternatives as Wilcoxon's test may completely break down for important classes of tail alternatives, the new tests have high and stable power. The new tests have also higher power than data driven rank tests for the unconstrained two-sample problem. Theoretical support is obtained by proving consistency of the new tests against very large classes of alternatives, including all common tail alternatives. A simple but accurate approximation of the null distribution makes application of the new tests easy.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 1999

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1504
    ISSN (Print)0169-2690

    Keywords

    • IR-65692
    • MSC-62E25
    • MSC-62G10
    • MSC-62G20
    • EWI-3324

    Cite this

    Albers, WW., Kallenberg, W. C. M., & Martini, F. (1999). Data driven rank tests for classes of tail alternatives. Enschede: University of Twente, Department of Applied Mathematics.
    Albers, Willem/Wim ; Kallenberg, W.C.M. ; Martini, F. / Data driven rank tests for classes of tail alternatives. Enschede : University of Twente, Department of Applied Mathematics, 1999.
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    title = "Data driven rank tests for classes of tail alternatives",
    abstract = "Tail alternatives describe the frequent occurrence of a non-constant shift in the two-sample problem with a shift function increasing in the tail. The classes of shift functions can be built up using Legendre polynomials. It is important to rightly choose the number of polynomials involved. Here this choice is based on the data, using a modification of Schwarz's selection rule. Given the data driven choice of the model, appropriate rank tests are applied. Simulations show that the new data driven rank tests work very well. While other tests for detecting shift alternatives as Wilcoxon's test may completely break down for important classes of tail alternatives, the new tests have high and stable power. The new tests have also higher power than data driven rank tests for the unconstrained two-sample problem. Theoretical support is obtained by proving consistency of the new tests against very large classes of alternatives, including all common tail alternatives. A simple but accurate approximation of the null distribution makes application of the new tests easy.",
    keywords = "IR-65692, MSC-62E25, MSC-62G10, MSC-62G20, EWI-3324",
    author = "Willem/Wim Albers and W.C.M. Kallenberg and F. Martini",
    note = "Imported from MEMORANDA",
    year = "1999",
    language = "Undefined",
    publisher = "University of Twente, Department of Applied Mathematics",
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    Albers, WW, Kallenberg, WCM & Martini, F 1999, Data driven rank tests for classes of tail alternatives. University of Twente, Department of Applied Mathematics, Enschede.

    Data driven rank tests for classes of tail alternatives. / Albers, Willem/Wim; Kallenberg, W.C.M.; Martini, F.

    Enschede : University of Twente, Department of Applied Mathematics, 1999.

    Research output: Book/ReportReportOther research output

    TY - BOOK

    T1 - Data driven rank tests for classes of tail alternatives

    AU - Albers, Willem/Wim

    AU - Kallenberg, W.C.M.

    AU - Martini, F.

    N1 - Imported from MEMORANDA

    PY - 1999

    Y1 - 1999

    N2 - Tail alternatives describe the frequent occurrence of a non-constant shift in the two-sample problem with a shift function increasing in the tail. The classes of shift functions can be built up using Legendre polynomials. It is important to rightly choose the number of polynomials involved. Here this choice is based on the data, using a modification of Schwarz's selection rule. Given the data driven choice of the model, appropriate rank tests are applied. Simulations show that the new data driven rank tests work very well. While other tests for detecting shift alternatives as Wilcoxon's test may completely break down for important classes of tail alternatives, the new tests have high and stable power. The new tests have also higher power than data driven rank tests for the unconstrained two-sample problem. Theoretical support is obtained by proving consistency of the new tests against very large classes of alternatives, including all common tail alternatives. A simple but accurate approximation of the null distribution makes application of the new tests easy.

    AB - Tail alternatives describe the frequent occurrence of a non-constant shift in the two-sample problem with a shift function increasing in the tail. The classes of shift functions can be built up using Legendre polynomials. It is important to rightly choose the number of polynomials involved. Here this choice is based on the data, using a modification of Schwarz's selection rule. Given the data driven choice of the model, appropriate rank tests are applied. Simulations show that the new data driven rank tests work very well. While other tests for detecting shift alternatives as Wilcoxon's test may completely break down for important classes of tail alternatives, the new tests have high and stable power. The new tests have also higher power than data driven rank tests for the unconstrained two-sample problem. Theoretical support is obtained by proving consistency of the new tests against very large classes of alternatives, including all common tail alternatives. A simple but accurate approximation of the null distribution makes application of the new tests easy.

    KW - IR-65692

    KW - MSC-62E25

    KW - MSC-62G10

    KW - MSC-62G20

    KW - EWI-3324

    M3 - Report

    BT - Data driven rank tests for classes of tail alternatives

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

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    Albers WW, Kallenberg WCM, Martini F. Data driven rank tests for classes of tail alternatives. Enschede: University of Twente, Department of Applied Mathematics, 1999.