Abstract: 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. (Joint work with Yingying Fan, Xiao Han and Jinchi Lv)

Bio: Jianqing Fan, is a statistician, financial econometrician, and data scientist. He is Frederick L. Moore '18 Professor of Finance, Professor of Statistics, and Professor of Operations Research and Financial Engineering at the Princeton University where he chaired the department from 2012 to 2015. He is the winner of The 2000 COPSS Presidents' Award, Morningside Gold Medal for Applied Mathematics (2007), Guggenheim Fellow (2009), Pao-Lu Hsu Prize (2013) and Guy Medal in Silver (2014). He got elected to Academician from Academia Sinica in 2012.

Fan is interested in statistical theory and methods in data science, statistical machine learning , finance, economics, computational biology, biostatistics with particular skills on high-dimensional statistics, nonparametric modeling, longitudinal and functional data analysis, nonlinear, survival analysis, time series, wavelets , among others.[1]

Jianqing Fan is a joint editor of Journal of Business and Economics Statistics and an associate editor of Management Science (2018--), among others, was the co-editor(-in-chief) of the Annals of Statistics (2004-2006) and an editor of Probability Theory and Related Fields (2003-2005), Econometrical Journal (2007-2012), Journal of Econometrics (2012-2018; managing editor 2014-18), and on the editorial boards of a number of other journals, including Journal of the American Statistical Association (1996-2017), Econometrica (2010-2013), Annals of Statistics (1998-2003), Statistica Sinica (1996-2002), and Journal of Financial Econometrics (2009-2012). He was the past president of the Institute of Mathematical Statistics (2006-2009), and past president of the International Chinese Statistical Association (2008-2010).

After receiving his Ph.D. in Statistics from the University of California at Berkeley in 1989, he has been appointed as assistant, associate, and full professor at the University of North Carolina at Chapel Hill (1989-2003), and as professor at the University of California at Los Angeles (1997-2000), Professor of Statistics and Chairman at the Chinese University of Hong Kong (2000-2003), and professor at the Princeton University (2003-), where he directs the Committee of Statistical Studies since 2006 and chaired Department of Operations Research and Financial Engineering from 2012 to 2015. He was named Frederick L. Moore'18 Professor of Finance since 2006

Fan has coauthored two highly-regarded books on Local Polynomial Modeling (1996) and Nonlinear time series: Parametric and Nonparametric Methods (2003) and authored or coauthored over 200 articles on finance, economics, statistical machine learning, computational biology, semiparametric and non-parametric modeling, nonlinear time series, survival analysis, longitudinal data analysis, and other aspects of theoretical and methodological statistics. He has been consistently ranked as a top 10 highly-cited mathematical scientist since the existence of such a ranking. His published work on statistics, financial econometrics, computational biology, and statistical machine learning has been recognized by the 2000 COPSS Presidents' Award, given annually to an outstanding statistician under age 40, invited speaker at The 2006 International Congress for Mathematicians, The Humboldt Research Award for lifetime achievement in 2006, The Morningside Gold Medal of Applied Mathematics in 2007, honoring triennially an outstanding applied mathematician of Chinese descent, Guggenheim Fellow in 2009, Pao-Lu Hsu Prize (2013), presented every three years by the International Chinese Statistical Association to individuals under the age of 50, Guy Medal in Silver (2014), presented once a year by Royal Statistical Society, and Noether Senior Scholar Award (2018), presented once a year by American Statistical Association, and the election to the fellow of American Association for the Advancement of Science, Institute of Mathematical Statistics, and American Statistical Association.