Uncertainty Quantification of MLE for Entity Ranking with Covariates
Jianqing Fan, Jikai Hou, Mengxin Yu.
Year: 2024, Volume: 25, Issue: 358, Pages: 1−83
Abstract
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.