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Statistica Sinica 22 (2012), 1305-1318





SPARSE PAIRED COMPARISONS IN THE

BRADLEY-TERRY MODEL


Ting Yan$^1$, Yaning Yang$^1$ and Jinfeng Xu$^2$


$^1$University of Science and Technology of China
and $^2$National University of Singapore


Abstract: When a group of subjects is repeatedly compared in pairs, the Bradley-Terry model is often used. By assuming that each pair has the same fixed number of comparison(s), Simons and Yao (1999) proved that the maximum likelihood estimates of the parameters retain good asymptotic properties when the number of subjects goes to infinity. In many applications, however, paired comparisons may be sparse and only exist in some pairs. In this note, we show that under a simple condition that controls sparsity, asymptotic results similar to Simons and Yao's continue to hold. Simulation studies and an application are further provided for the illustration of the sparsity condition and the asymptotic results.



Key words and phrases: Bradley-Terry model, maximum likelihood estimate, paired comparisons, sparsity.

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