报告人：Jianqing Fan
报告地点：惟真楼523
报告时间：2024年08月01日星期四10:30-11:30
报告摘要：
Network data is prevalent in numerous big data applications, including economics and health networks, where it is of prime importance to understand the latent structure of the network. In this paper, we model the network using the Degree-Corrected Mixed Membership (DCMM) model. In the DCMM model, for each node i, there exists a membership vector consisting of the weight that node i puts in community k. We derive novel finite-sample expansion for the weights, which allows us to obtain asymptotic distributions and confidence intervals of the membership mixing probabilities and other related population quantities. This fills an important gap in uncertainty quantification on the membership profile. We further develop a ranking scheme of the vertices based on the membership mixing probabilities on specific communities and perform relevant statistical inferences. A multiplier bootstrap method is proposed for ranking inference of individual members' profiles with respect to a given community. The validity of our theoretical results is further demonstrated via numerical experiments in both real and synthetic data examples. (Joint work with Sohom Bhattacharya and Jikai Hou)
主讲人简介：
Jianqing Fan is Frederick L. Moore Professor of Finance, Former Chairman of Department of Operations Research and Financial Engineering at Princeton University. He was the past president of the Institute of Mathematical Statistics and the 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, PTRF and etc. His published work on statistics, machine learning and finance 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 member of Royal Academy of Belgium, and follow of American Associations for Advancement of Science, Institute of Mathematical Statistics, American Statistical Association and Society of Financial Econometrics.
