Detecting positive quadrant dependence and positive function dependence

A. Janic-Wróblewska, W.C.M. Kallenberg, T. Ledwina

    Research output: Book/ReportReportProfessional

    37 Downloads (Pure)

    Abstract

    There is a lot of interest in positive dependence going beyond linear correlation. In this paper three new rank tests for testing independence against positive dependence are introduced. The first one is directed on positive quadrant dependence, the second and third one concentrate on positive function dependence. The new testing procedures are not only sensitive for positive grade linear correlation, but also for positive grade correlations of higher order. They are based on the principle of data driven tests, which consists of three steps. Firstly, parametric families are introduced spanning up the space of null hypothesis and alternatives; secondly, within the families good tests are used; thirdly, a selection rule determines the appropriate model. The new tests improve standard tests for linear correlation as Spearman's rank correlation test substantially in case some proper higher order correlations are exhibited by the data, while the loss in power under alternatives with dominating linear correlation is not very high. Monte Carlo results clearly show this behavior.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    Number of pages27
    Publication statusPublished - 2003

    Publication series

    NameMemorandum Faculty of Mathematical Sciences
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1689
    ISSN (Print)0169-2690

    Keywords

    • MSC-62G10
    • MSC-62H20
    • IR-65874
    • EWI-3509
    • METIS-213197
    • MSC-65C05

    Cite this

    Janic-Wróblewska, A., Kallenberg, W. C. M., & Ledwina, T. (2003). Detecting positive quadrant dependence and positive function dependence. (Memorandum Faculty of Mathematical Sciences; No. 1689). Enschede: University of Twente, Faculty of Mathematical Sciences.
    Janic-Wróblewska, A. ; Kallenberg, W.C.M. ; Ledwina, T. / Detecting positive quadrant dependence and positive function dependence. Enschede : University of Twente, Faculty of Mathematical Sciences, 2003. 27 p. (Memorandum Faculty of Mathematical Sciences; 1689).
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    abstract = "There is a lot of interest in positive dependence going beyond linear correlation. In this paper three new rank tests for testing independence against positive dependence are introduced. The first one is directed on positive quadrant dependence, the second and third one concentrate on positive function dependence. The new testing procedures are not only sensitive for positive grade linear correlation, but also for positive grade correlations of higher order. They are based on the principle of data driven tests, which consists of three steps. Firstly, parametric families are introduced spanning up the space of null hypothesis and alternatives; secondly, within the families good tests are used; thirdly, a selection rule determines the appropriate model. The new tests improve standard tests for linear correlation as Spearman's rank correlation test substantially in case some proper higher order correlations are exhibited by the data, while the loss in power under alternatives with dominating linear correlation is not very high. Monte Carlo results clearly show this behavior.",
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    series = "Memorandum Faculty of Mathematical Sciences",
    publisher = "University of Twente, Faculty of Mathematical Sciences",
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    Janic-Wróblewska, A, Kallenberg, WCM & Ledwina, T 2003, Detecting positive quadrant dependence and positive function dependence. Memorandum Faculty of Mathematical Sciences, no. 1689, University of Twente, Faculty of Mathematical Sciences, Enschede.

    Detecting positive quadrant dependence and positive function dependence. / Janic-Wróblewska, A.; Kallenberg, W.C.M.; Ledwina, T.

    Enschede : University of Twente, Faculty of Mathematical Sciences, 2003. 27 p. (Memorandum Faculty of Mathematical Sciences; No. 1689).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Detecting positive quadrant dependence and positive function dependence

    AU - Janic-Wróblewska, A.

    AU - Kallenberg, W.C.M.

    AU - Ledwina, T.

    N1 - Imported from MEMORANDA

    PY - 2003

    Y1 - 2003

    N2 - There is a lot of interest in positive dependence going beyond linear correlation. In this paper three new rank tests for testing independence against positive dependence are introduced. The first one is directed on positive quadrant dependence, the second and third one concentrate on positive function dependence. The new testing procedures are not only sensitive for positive grade linear correlation, but also for positive grade correlations of higher order. They are based on the principle of data driven tests, which consists of three steps. Firstly, parametric families are introduced spanning up the space of null hypothesis and alternatives; secondly, within the families good tests are used; thirdly, a selection rule determines the appropriate model. The new tests improve standard tests for linear correlation as Spearman's rank correlation test substantially in case some proper higher order correlations are exhibited by the data, while the loss in power under alternatives with dominating linear correlation is not very high. Monte Carlo results clearly show this behavior.

    AB - There is a lot of interest in positive dependence going beyond linear correlation. In this paper three new rank tests for testing independence against positive dependence are introduced. The first one is directed on positive quadrant dependence, the second and third one concentrate on positive function dependence. The new testing procedures are not only sensitive for positive grade linear correlation, but also for positive grade correlations of higher order. They are based on the principle of data driven tests, which consists of three steps. Firstly, parametric families are introduced spanning up the space of null hypothesis and alternatives; secondly, within the families good tests are used; thirdly, a selection rule determines the appropriate model. The new tests improve standard tests for linear correlation as Spearman's rank correlation test substantially in case some proper higher order correlations are exhibited by the data, while the loss in power under alternatives with dominating linear correlation is not very high. Monte Carlo results clearly show this behavior.

    KW - MSC-62G10

    KW - MSC-62H20

    KW - IR-65874

    KW - EWI-3509

    KW - METIS-213197

    KW - MSC-65C05

    M3 - Report

    T3 - Memorandum Faculty of Mathematical Sciences

    BT - Detecting positive quadrant dependence and positive function dependence

    PB - University of Twente, Faculty of Mathematical Sciences

    CY - Enschede

    ER -

    Janic-Wróblewska A, Kallenberg WCM, Ledwina T. Detecting positive quadrant dependence and positive function dependence. Enschede: University of Twente, Faculty of Mathematical Sciences, 2003. 27 p. (Memorandum Faculty of Mathematical Sciences; 1689).