Least squares for cardinal paired comparisons data
严格分析了带协变量和不带协变量的基数配对比较数据图模型的最小二乘估计量，给出了保证估计排名强相合性、渐近正态性和指数收敛性的图论充要条件，并应用于NBA球队排名。
Abstract 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.