Grouped sparse paired comparisons in the Bradley-Terry model

Details Grouped sparse paired comparisons in the Bradley-Terry model Grouped sparse paired comparisons in the Bradley-Terry model

2011-11-22

arxiv.org/abs/1111.5110v1

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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 and most regular seasons under NCAA. Motivated by these situations, we propose two types of group sparsity for paired comparisons and show the consistency and asymptotical normality of the maximum likelihood estimate in the Bradley-Terry model under one type of group sparsity and derive the consistency under the other type of group sparsity with more sparse intergroup comparisons when the number of parameters goes to infinity in this paper. Simulations and a data example are carried out to illustrate the group sparsity and asymptotical results.

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