Uncertainty Quantification of MLE for Entity Ranking with Covariates

Jianqing Fan; Jikai Hou; Mengxin Yu

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.

Uncertainty Quantification of MLE for Entity Ranking with Covariates

Abstract