Nonparametric Estimation in the Dynamic Bradley-Terry Model
This work addresses the challenge of ranking teams over time in sparse settings, which is incremental as it builds on the Bradley-Terry model with kernel smoothing and new theoretical guarantees.
The authors tackled the problem of estimating dynamic global rankings from pairwise comparisons by proposing a time-varying generalization of the Bradley-Terry model with nonparametric modeling, and they derived oracle bounds for estimation error and excess risk, achieving competitive performance in simulations and real-world data.
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.