A General Pairwise Comparison Model for Extremely Sparse Networks

• 成果类型: Article
• 署名作者: Han, Ruijian; Xu, Yiming; Chen, Kani
• 署名单位: Chinese University of Hong Kong; Utah System of Higher Education; University of Utah; Hong Kong University of Science & Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2053137
• 发表日期: 2023
• 页码: 2422-2432
• 关键词: limited information estimation; paired-comparison data; bradley-terry model; thurstonian models; ranking; TIES

摘要

Statistical estimation using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this article, we propose a general framework to model the mutual interactions in a network, which enjoys ample flexibility in terms of model parameterization. Under this setup, we show that the maximum likelihood estimator for the latent score vector of the subjects is uniformly consistent under a near-minimal condition on network sparsity. This condition is sharp in terms of the leading order asymptotics describing the sparsity. Our analysis uses a novel chaining technique and illustrates an important connection between graph topology and model consistency. Our results guarantee that the maximum likelihood estimator is justified for estimation in large-scale pairwise comparison networks where data are asymptotically deficient. Simulation studies are provided in support of our theoretical findings. Supplementary materials for this article are available online.