Abstract
Ranking from pairwise comparisons is a central problem in a wide range of learning and social contexts, and the Bradley-Terry-Luce (BTL) model is one of the most studied models for analyzing ranking data. Despite all the recent progress, uncertainty quantification under the BTL model remains unclear when only a small number of comparisons is observed. To address this challenge, we first establish non-asymptotic entrywise distributions of the maximum likelihood estimation and the spectral method under the BTL model. We then develop statistical inference procedures for individual rankings and preference parameters.