Least squares for cardinal paired comparisons data

• 成果类型: Article; Early Access
• 署名作者: Singh, Rahul; Iliopoulos, George; Davidov, Ori
• 署名单位: Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Delhi; University of Piraeus; University of Haifa
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf035
• 发表日期: 2025
• 关键词: bradley-terry models; ranking; transitivity; estimators; matrix; minors; mle

摘要

Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analysed. Novel, graph-based, necessary, and sufficient conditions that guarantee strong consistency, asymptotic normality, and the exponential convergence of the estimated ranks are emphasized. A complete theory for models with covariates is laid out. In particular, conditions under which covariates can be safely omitted from the model are provided. The methodology is employed in the analysis of both finite and infinite sets of ranked items where the case of large sparse comparison graphs is addressed. The proposed methods are explored by simulation and applied to the ranking of teams in the National Basketball Association.