Grouped sparse paired comparisons in the Bradley-Terry model

TL;DR

This paper introduces a group sparsity approach for paired comparison models like Bradley-Terry, addressing scenarios with dense within-group and sparse between-group comparisons, and proves the statistical properties of the estimators.

Contribution

It proposes a novel group sparsity framework for paired comparisons and establishes the consistency and asymptotic normality of the maximum likelihood estimator.

Findings

Simulations confirm the theoretical properties.

The model effectively captures group structures in comparisons.

Estimates are consistent and asymptotically normal.

Abstract

In a wide class of paired comparisons, especially in the sports games, in which all subjects are divided into several groups, the intragroup comparisons are dense and the intergroup comparisons are sparse. Typical examples include the NFL regular season. Motivated by these situations, we propose group sparsity for paired comparisons and show the consistency and asymptotical normality of the maximum likelihood estimate in the Bradley-Terry model when the number of parameters goes to infinity in this paper. Simulations are carried out to illustrate the group sparsity and asymptotical results.