# Nonparametric Estimation in the Dynamic Bradley-Terry Model

arXiv: https://arxiv.org/abs/2003.00083 · HTML: https://mlsanity.com/paper/2003.00083/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2020.

## Built on by (most cited first, 8 of 8)

- [Right Now, Wrong Then: Non-Stationary Direct Preference Optimization under Preference Drift](https://mlsanity.com/paper/2407.18676/) (2024)
- [Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method](https://mlsanity.com/paper/2109.13743/) (2021)
- [Dynamic Ranking and Translation Synchronization](https://mlsanity.com/paper/2207.01455/) (2022)
- [Minimax Hypothesis Testing for the Bradley-Terry-Luce Model](https://mlsanity.com/paper/2410.08360/) (2024)
- [Hypothesis Testing for Generalized Thurstone Models](https://mlsanity.com/paper/2512.02912/) (2025)
- [Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries](https://mlsanity.com/paper/2605.23854/) (2026)
- [Dynamic angular synchronization under smoothness constraints](https://mlsanity.com/paper/2406.04071/) (2024)
- [Preference-Based Dynamic Ranking Structure Recognition](https://mlsanity.com/paper/2509.24493/) (2025)

## Abstract (arXiv)

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.