主题：Ranking Inferences Based on the Top Choice of Multiway Comparisons

报告人：Jianqing FAN, Frederick L. Moore Professor of Finance, Professor of Operations Research and Financial Engineering, Former Chairman of Department of Operations Research and Financial Engineering and Director of Committee of Statistical Studies, Princeton University

主持人：Jianhua HUANG, Presidential Chair Professor & Associate Dean (Faculty Affairs and Strategic Operations), School of Data Science, CUHK-Shenzhen

日期：25 October (Wednesday), 2023

时间：14:30 - 15:30, Beijing Time

形式：Offline

线下地点：103 Meeting Room, Daoyuan Building.

语言：English

摘要：

This talk considers ranking inference of n items based on the observed data on the top choice among M randomly selected items at each trial. This is a useful modification of the Plackett-Luce model for M-way ranking with only the top choice observed and is an extension of the celebrated Bradley-Terry-Luce model that corresponds to M = 2. 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 underlying n preference scores using both l2-norm and l∞-norm, with the mini- mum sampling complexity. In addition, we establish the asymptotic normality of the maximum likelihood estimator that allows us to construct confidence intervals for the underlying scores. Furthermore, we propose a novel inference framework for ranking items through a sophisticated maximum pairwise difference statistic whose distribution is estimated via a valid Gaussian multi- plier bootstrap. The estimated distributions are then used to construct simultaneous confidence intervals for the differences in the preference scores and the ranks of individual items. They also enable us to address various inference questions on the ranks of these items. Extensive simula- tion studies lend further support to our theoretical results. A real data application illustrates the usefulness of the proposed methods convincingly.

(Joint work with Zhipeng Lou,  Weichen Wang, and Mengxin Yu)

简介：

Jianqing Fan is Frederick L. Moore Professor of Finance, Professor of Operations Research and Financial Engineering, Former Chairman of Department of Operations Research and Financial Engineering and Director of Committee of Statistical Studies at Princeton University, where he directs both financial econometrics and statistics labs.  After receiving his Ph.D. from the University of California at Berkeley, he has been appointed as assistant, associate, and full professor at the University of North Carolina at Chapel Hill (1989-2003), professor at the University of California at Los Angeles (1997-2000), professor and chair at Chinese University of Hong Kong, and professor at the Princeton University (2003--). He was the past president of the Institute of Mathematical Statistics and International Chinese Statistical Association. He is the joint editor of Journal of American Statistical Association and was the co-editor of The Annals of Statistics, Probability Theory and Related Fields, Econometrics Journal,  Journal of Econometrics, and Journal of Business and Economics Statistics.

His published work on statistics, machine learning, economics, finance, and computational biology has been recognized by The 2000 COPSS Presidents' Award, The 2007 Morningside Gold Medal of Applied Mathematics, Guggenheim Fellow in 2009, P.L. Hsu Prize in 2013, Royal Statistical Society Guy medal in silver  in 2014,  Noether Distinguished Scholar Award in 2018, Le Cam Award and Lecture in 2021, and election to Academician of Academia Sinica and follow of American Associations for Advancement of Science, Institute of Mathematical Statistics, American Statistical Association, and Society of Financial Econometrics.  His research interest includes high-dimensional statistics, data science, machine learning, financial econometrics, and computational biology.