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    ON TOURNAMENTS AND NEGATIVE DEPENDENCE

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    MR_R2_25_8_2022_v2.pdf (379.3Kb)
    Links to Files
    https://pluto.huji.ac.il/~rinott/publications/MR_R2_25_8_2022_v2.pdf
    Permanent Link
    http://hdl.handle.net/11603/26125
    Collections
    • UMBC Faculty Collection
    • UMBC Mathematics and Statistics Department
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    Author/Creator
    MALINOVSKY, YAAKOV
    RINOTT, YOSEF
    Author/Creator ORCID
    https://orcid.org/0000-0003-2888-674X
    Date
    2022-08-25
    Type of Work
    16 pages
    Text
    journal articles
    preprints
    Rights
    This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
    Abstract
    Negative dependence of sequences of random variables is often an interesting characteristic of their distribution, as well as a useful tool for studying various asymptotic results, including central limit theorems, Poisson approximations, the rate of increase of the maximum, and more. In the study of probability models of tournaments, negative dependence of participants’ outcomes arises naturally with application to various asymptotic results. In particular, the property of negative orthant dependence was proved in several articles for different tournament models, with a special proof for each model. In this note we unify these results by proving a stronger property, negative association, a generalization leading to a very simple proof. We also present a natural example of a knockout tournament where the scores are negatively orthant dependent but not negatively associated. The proof requires a new result on a preservation property of negative orthant dependence that is of independent interest.


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3021


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.