报告题目：基于多元比较的排序推断
报告人：王炜辰 助理教授 香港大学
报告时间：2024年7月24日（周三），上午11:00
报告地点：兴庆校区数学楼2-2会议室
报告摘要：This research considers ranking inference of n items based on the observed ranking results among multiple selected items at each trial. Two classical methods exist: the maximum likelihood estimator (MLE) and the spectral estimator. For the MLE, under a uniform sampling scheme in which any M distinguished items are selected for comparisons with probability p and the selected M items are compared L times with multinomial outcomes, we establish the statistical rates of convergence for the underlying n preference scores, with the minimum sampling complexity. For the spectral estimator, we can work with a very general and more realistic setup in which the comparison graph consists of hyper-edges of possible heterogeneous sizes and the number of comparisons can be as low as one for a given hyper-edge. In addition, we establish the asymptotic normality for both methods that allows us to construct confidence intervals for the underlying scores. We also unravel the relationship between the spectral estimator and the MLE. Given the asymptotic distributions of the estimated preference scores, we then introduce a novel framework to carry out both one-sample and two-sample inferences on ranks, applicable to both fixed and random graph settings. This comprehensive framework relies on a sophisticated maximum pairwise difference statistic whose distribution is estimated via a valid Gaussian multiplier bootstrap. Finally, we substantiate our findings with comprehensive numerical simulations and subsequently apply our developed methodologies to perform statistical inferences on statistics journals and movie rankings.
个人简介：王炜辰，香港大学经管学院创新与信息管理系助理教授。博士毕业于普林斯顿大学运筹与金融工程系，师承范剑青教授，曾任职于量化对冲基金Two Sigma Investments，期间担任普林斯顿大学金融计量课程访问讲师，本科毕业于清华大学数学物理基础科学专业。研究兴趣包括计量因子模型、高维统计推断、鲁棒统计量、以及机器学习在金融数据的应用，研究工作发表于Annals of Statistics, Journal of Machine Learning Research, Journal of Econometrics等期刊。
