English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The Bradley-Terry-Luce (BTL) model is a benchmark model for pairwisecomparisons between individuals. Despite recent progress on the first-orderasymptotics of several popular procedures, the understanding of uncertaintyquantification in the BTL model remains largely incomplete, especially when theunderlying comparison graph is sparse. In this paper, we fill this gap byfocusing on two estimators that have received much recent attention: themaximum likelihood estimator (MLE) and the spectral estimator. Using a unifiedproof strategy, we derive sharp and uniform non-asymptotic expansions for bothestimators in the sparsest possible regime (up to some poly-logarithmicfactors) of the underlying comparison graph. These expansions allow us toobtain: (i) finite-dimensional central limit theorems for both estimators; (ii)construction of confidence intervals for individual ranks; (iii) optimalconstant of $\ell_2$ estimation, which is achieved by the MLE but not by thespectral estimator. Our proof is based on a self-consistent equation of thesecond-order remainder vector and a novel leave-two-out analysis.

Uncertainty quantification in the Bradley-Terry-Luce model