Year: 2025
Type: article
Abstract: Negative dependence in tournaments has received attention in the literature. The property of negative orthant dependence (NOD) was proved for different tournament models with a special proof for each model. For general round-robin tournaments and knockout tournaments with random draws, Malinovsky and Rinott (2023) unified and simplified many existing results in the literature by proving a stronger property, negative association (NA). For a knockout tournament with a non-random draw, they presented an example to illustrate that bold italic upper S S ${\boldsymbol{S}}$ is NOD but not NA. However, their proof is not correct. In this paper, we establish the properties of negative regression dependence (NRD), negative left-tail dependence (NLTD), and negative right-tail dependence (NRTD) for a knockout tournament with a random draw and with players being of equal strength. For a knockout tournament with a non-random draw and with equal strength, we prove that bold italic upper S S ${\boldsymbol{S}}$ is NA and NRTD, while bold italic upper S S ${\boldsymbol{S}}$ is, in general, not NRD or NLTD.
Source: Journal of Applied Probability
Authors: Yuting Su, Zhenfeng Zou, Taizhong Hu
Institution: University of Science and Technology of China
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416982927