Pairwise comparison models have been widely used for utility evaluation and ranking across various fields. The increasing scale of problems today underscores the need to understand statistical inference in these models when the number of subjects diverges, a topic currently lacking in the literature except in a few special instances. To partially address this gap, this paper establishes a near-optimal asymptotic normality result for the maximum likelihood estimator in a broad class of pairwise comparison models, as well as a non-asymptotic convergence rate for each individual subject under comparison. The key idea lies in identifying the Fisher information matrix as a weighted graph Laplacian, which can be studied via a meticulous spectral analysis. Our findings provide a unified theory for performing statistical inference in a wide range of pairwise comparison models beyond the Bradley--Terry model, benefiting practitioners with theoretical guarantees 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：成对比较模型已被广泛应用于各领域的效用评估与排名。当前问题规模的日益增长凸显了当比较对象数量发散时理解这些模型中统计推断的必要性——除少数特例外，这一主题在现有文献中尚属空白。为部分填补这一空白，本文针对一大类成对比较模型建立了最大似然估计量的近最优渐近正态性结果，并为每个待比较个体给出了非渐近收敛速率。其核心思想在于将Fisher信息矩阵识别为加权图拉普拉斯算子，并通过精细的谱分析对其展开研究。我们的研究成果为超越Bradley-Terry模型的广泛成对比较模型提供了统一的统计推断理论框架，为实践者使用这些模型提供了理论保障。通过合成数据模拟验证了渐近正态性结果，并基于网球比赛数据集进行了假设检验。