ON TOURNAMENTS AND NEGATIVE DEPENDENCE
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http://hdl.handle.net/11603/26125Metadata
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Date
2022-08-25Type of Work
16 pagesText
journal articles
preprints
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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.