A0444
Title: A unified analysis of likelihood-based estimators in the Plackett-Luce model
Authors: Ruijian Han - The Hong Kong Polytechnic University (China) [presenting]
Abstract: The Plackett-Luce model has been extensively used for rank aggregation in social choice theory. A central question in this model concerns estimating the utility vector that governs the model's likelihood. The asymptotic theory of utility vector estimation is investigated by maximizing different types of likelihood, such as full, marginal, and quasi-likelihood. Starting from interpreting the estimating equations of these estimators to gain some initial insights, their asymptotic behavior is analyzed as the number of compared objects increases. In particular, both the uniform consistency and asymptotic normality of these estimators are established, and the trade-off between statistical efficiency and computational complexity is discussed. For generality, the results are proven for deterministic graph sequences under appropriate graph topology conditions. These conditions are shown to be revealing and sharp when applied to common sampling scenarios, such as nonuniform random hypergraph models and hypergraph stochastic block models. Numerical results are provided to support the findings.
