Stat Colloquium [In-person]: Dr. Yaakov Malinovsky

Title: Negative dependence notions and tournament scores

Abstract: Negative dependence of sequences of random variables is an interesting characteristic of their distribution and 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. We unify and simplify these results by proving a stronger property: negative association. 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.