论文标题
动态bradley-terry模型中的非参数估计
Nonparametric Estimation in the Dynamic Bradley-Terry Model
论文作者
论文摘要
我们提出了Bradley-Terry模型的时变概括，该模型允许对不同团队的动态全球排名进行非参数建模。我们开发了一个新颖的估计器，该估计器依赖于内核平滑来预处理过程，随着时间的流逝，对成对的比较，并且适用于Bradley-Terry可能不合适的稀疏设置。我们为估计量的存在和独特性获得了必要和充分的条件。我们还为估计误差和多余的风险而得出了随时间变化的甲骨文界限，在模型 - 不合时宜的设置中，布拉德利 - 泰式模型不一定是真实的数据生成过程。我们使用模拟和现实世界数据彻底测试了模型的实际有效性，并提出了一种有效的数据驱动方法来进行带宽调整。
We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams. We develop a novel estimator that relies on kernel smoothing to pre-process the pairwise comparisons over time and is applicable in sparse settings where the Bradley-Terry may not be fit. We obtain necessary and sufficient conditions for the existence and uniqueness of our estimator. We also derive time-varying oracle bounds for both the estimation error and the excess risk in the model-agnostic setting where the Bradley-Terry model is not necessarily the true data generating process. We thoroughly test the practical effectiveness of our model using both simulated and real world data and suggest an efficient data-driven approach for bandwidth tuning.
