报告题目【Statistical Inference on Membership Profiles in Large Networks】
时间：2019年9月29日 (星期日) 上午09:00
地点：福建师范大学行政楼附二楼宏达厅
主讲：美国普林斯顿大学教授，范剑青
主办：数学与信息学院
参加对象：相关教师和研究生
报告人简介：美国普林斯顿大学终身教授、国际数理统计学会前主席，国家级特聘专家，“中央研究院”院士，Frederick L. Moore'18 金融教授，香港中文大学统计系讲座教授和统计系前任主任，复旦大学大数据学院、大数据研究院、大学金融研究院院长，上海大数据金融创新中心主任，上海大数据金融实验室主任。荣获2000年度的COPSS总统奖，2006年获得国家杰出海外青年基金。2007年荣获“晨兴华人数学家大会应用数学金奖”，2012年当选中央研究院院士，2013年获泛华统计学会的“许宝禄奖”，2014年荣获英国皇家统计学会的“Guy 奖”的银质奖章。此外，范剑青教授是美国科学促进会(AAAS)、美国统计学会(ASA)、国际数理统计学会(IMS)，计量金融学会（SOFIE）的会士，以及国际顶尖统计期刊《The Annals of Statistics统计年鉴》，《Probability Theory and Related Fields概率及其相关领域统》等的前主编等，《Journal of Econometrics计量经济杂志》的主编。出版过《Nonlinear Time Series》、《New developments in biostatistics and bioinformatics》及《Nonlinear time series nonparametric and parametric methods》等书籍。范剑青教授的主要研究兴趣为大数据，计量经济和金融、金融工程、机器学习、高维统计、时间序列、非参数建模、概率理论等。
报告摘要：Network data is prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. The nodes can be broadly defined such as individuals, economic entities, documents, or medical disorders in social, economic, text, or health networks. Yet a simple question of how to precisely quantify the statistical uncertainty associated with the identification of latent links still remains largely unexplored. In this talk, we suggest the method of statistical inference on membership profiles in large networks (SIMPLE) in the setting of degree-corrected mixed membership model, where the null hypothesis assumes that the pair of nodes share the same profile of community memberships. In the simpler case of no degree heterogeneity, the model reduces to the mixed membership model and an alternative more robust test is proposed. Under some mild regularity conditions, we establish the exact limiting distributions of the two forms of SIMPLE test statistics under the null hypothesis and their asymptotic properties under the alternative hypothesis. Both forms of SIMPLE tests are pivotal and have asymptotic size at the desired level and asymptotic power one. The advantages and practical utility of our new method in terms of both size and power are demonstrated through several simulation examples and real network applications.
