Asymptotics when the number of parameters tends to infinity in the Bradley-Terry model for paired comparisons
Bradley–Terry 配对比较模型中参数个数趋于无穷时的渐近理论
We are concerned here with establishing the consistency and asymptotic normality for the maximum likelihood estimator of a “merit vector” $(u_0,\dots,u_t)$, representing the merits of $t +1$ teams (players, treatments, objects), under the Bradley–Terry model, as $t \to \infty$. This situation contrasts with the well-known Neyman–Scott problem under which the number of parameters grows with $t$ (the amount of sampling), and for which the maximum likelihood estimator fails…