Tests on Dynamic Ranking

In this paper, we investigate the dynamic Bradley-Terry model, a highly acclaimed statistical ranking model, and tackle several crucial inference problems related to score functions and rank properties.Specifically, we tackle the test problems of score function variation and pairwise similarity, providing valuable insights for model determination and simplification.We derive asymptotic null distributions for the proposed test statistics and prove the tests' consistency.Furthermore, we introduce a novel confidence band of dynamic rank and establish an innovative and generally applicable test framework for dynamic ranking properties.To overcome the conservativeness issue brought by the supreme form statistics, we introduce a novel approach based on signed score difference statistics for ranking inferences.We present theoretical guarantees for the proposed scheme.Numerical simulations validate the theories and demonstrate the satisfactory performance of our methods.The proposed methods are applied to a real dataset, yielding insightful results.