Pairwise comparison models are used for quantitatively evaluating utility and ranking in various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the number of subjects diverges, which is currently lacking in the literature except in a few special instances. This paper addresses this gap by establishing an asymptotic normality result for the maximum likelihood estimator in a broad class of pairwise comparison models. The key idea lies in identifying the Fisher information matrix as a weighted graph Laplacian matrix which can be studied via a meticulous spectral analysis. Our findings provide the first unified theory for performing statistical inference in a wide range of pairwise comparison models beyond the Bradley--Terry model, benefiting practitioners with a solid theoretical guarantee for their use. Simulations utilizing synthetic data are conducted to validate the asymptotic normality result, followed by a hypothesis test using a tennis competition dataset.

翻译：成对比较模型用于在多个领域中对效用进行定量评估和排序。现代问题规模的不断扩大，凸显了在主体数量发散时理解这些模型中统计推断的必要性，而目前除少数特例外，文献中尚缺乏相关研究。本文通过建立一类广泛成对比较模型中最大似然估计的渐近正态性结果，填补了这一空白。其关键思想在于将费舍尔信息矩阵识别为加权图拉普拉斯矩阵，并通过精细的谱分析进行研究。我们的发现首次为超越布拉德利-特里模型的广泛成对比较模型提供了统一的统计推断理论，为实践者使用这些模型提供了坚实的理论保证。利用合成数据进行的仿真实验验证了渐近正态性结果，随后基于网球比赛数据集进行了假设检验。