Related papers: On Tournaments and Negative Dependence

In this paper we introduce several natural definitions of asymptotic independence of two sequences of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak…

Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…

Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the bracket, these results ignore the prevalent…

We establish a connection between dependence structures and subclasses of distortion riskmetrics under which the latter are additive. A new notion of positive dependence, called partial comonotonicity, is developed, which nests the existing…

Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.

We study the mathematical properties of probabilistic processes in which the independent actions of $n$ players (`causes') can influence the outcome of each player (`effects'). In such a setting, each pair of outcomes will generally be…

For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…

We consider $N$ events that are defined on a common probability space. Those events shell have a common probability function that is symmetric with respect to interchanging the events. We ask for the probability distribution of the number…

Model-free knockoffs is a recently proposed technique for identifying covariates that is likely to have an effect on a response variable. The method is an efficient method to control the false discovery rate in hypothesis tests for separate…

We prove that in a random tournament the events $\{s\rightarrow a\}$ and $\{t\rightarrow b\}$ are positively correlated, for distinct vertices $a,s,b,t \in K_n.$ It is also proven that the correlation between the events $\{s\rightarrow a\}$…

Tournaments are frequently used incentive mechanisms to enhance performance. In this paper, we use field data and show that skill disparities among contestants asymmetrically affect the performance of contestants. Skill disparities have…

We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global…

We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of…

Competitive tournaments appear in sports, politics, population ecology, and animal behavior. All of these fields have developed methods for rating competitors and ranking them accordingly. A tournament is intransitive if it is not…

We explore a new way to evaluate generative models using insights from evaluation of competitive games between human players. We show experimentally that tournaments between generators and discriminators provide an effective way to evaluate…

The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as…

Our model describes competition between groups driven by the choices of self-interested voters within groups. Within a Poisson voting environment, parties observe aggregate support from groups and can allocate prizes or punishments to them.…

In her recent paper [Negative dependence, scrambled nets, and variance bounds. Math. Oper. Res. 43 (2018), 228-251] Christiane Lemieux studied a framework to analyze the dependence structure of sampling schemes. The main goal of the…

Outcome-dependent sampling designs are common in many different scientific fields including epidemiology, ecology, and economics. As with all observational studies, such designs often suffer from unmeasured confounding, which generally…

We consider the problem of estimating the probability matrix governing a tournament or linkage in graphs from incomplete observations, under the assumption that the probability matrix satisfies natural monotonicity constraints after being…