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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.01971 |
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Table of Contents:
- 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, Malinovsky and Rinott (2023) presented an example to illustrate that 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 S is NA and NRTD, while S is, in general, not NRD or NLTD.