Uncertainty Quantification of MLE for Entity Ranking with Covariates

We study statistical estimation and inference for the ranking problems based on pairwise comparisons with additional covariate information. In specific, in this paper, we study a Covariate-Assisted Ranking Estimation (CARE) model in a systematic way, that extends the well-known Bradley-Terry-Luce (BTL) model by incorporating the covariate information. We impose natural identifiability conditions, derive the statistical rates for the MLE under a sparse comparison graph, and obtain its asymptotic distribution. Moreover, we validate our theoretical results through large-scale numerical studies.