The Bradley-Terry-Luce (BTL) model is a classic and very popular statistical approach for eliciting a global ranking among a collection of items using pairwise comparison data. In applications in which the comparison outcomes are observed as a time series, it is often the case that data are non-stationary, in the sense that the true underlying ranking changes over time. In this paper we are concerned with localizing the change points in a high-dimensional BTL model with piece-wise constant parameters. We propose novel and practicable algorithms based on dynamic programming that can consistently estimate the unknown locations of the change points. We provide consistency rates for our methodology that depend explicitly on the model parameters, the temporal spacing between two consecutive change points and the magnitude of the change. We corroborate our findings with extensive numerical experiments and a real-life example.
翻译:Bradley-Terri-Luece(BTL)模式是一种典型和非常流行的统计方法,用于利用对称比较数据对收集的项目进行全球排名。在将比较结果观察为一个时间序列的应用程序中,数据往往是非静止的,因为真正的基本等级随时间变化。在本文中,我们关心的是将高维BTL模型的变化点与小片不变参数进行本地化。我们提出基于动态编程的新颖和实用的算法,这些算法可以一致地估计变化点的未知位置。我们为我们的方法提供了一致性率,这种方法明确取决于模型参数、两个连续变化点之间的时间间隔以及变化的程度。我们用大量的数字实验和一个真实的范例来证实我们的调查结果。