Holder： Wei Lan (Southwestern University of Finance and Economics)
Location：Room 217, Guanghua Building 2
The stochastic block model (SBM) has been widely used to analyze network data. Various goodness-of-ﬁt tests have been proposed to assess the adequacy of model structures. To the best of our knowledge, however, none of the existing approaches are applicable for sparse networks in which the connection probability of any two communities is of order O( log n/n), and the number of communities is divergent. To ﬁll this gap, we propose a novel goodness-of ﬁt test for the stochastic block model. The key idea is to construct statistics by sampling the maximum entry-deviations of the adjacency matrix that the negative impacts of network sparsity are alleviated by the sampling process. We demonstrate theoretically that the proposed test statistic converges to the Type-I extreme value distribution under the null hypothesis regardless of the network structure. Accordingly, it can be applied to both dense and sparse networks. In addition, we obtain the asymptotic power against alternatives. Moreover, we introduce a bootstrap-corrected test statistic to improve the ﬁnite sample performance, recommend an augmented test statistic to increase the power, and extend the proposed test to the degree-corrected SBM. Simulation studies and two empirical examples with both dense and sparse networks indicate that the proposed method performs well.
About the Speaker:
兰伟，博士毕业于北京大学光华管理学院，现为西南财经大学教授，博士生导师，西南财经大学“光华杰出学者计划”青年杰出教授。主要研究方向为高维数据建模、大型网络数据分析和投资组合优化。主持国家自然科学基金面上项目和多个重点项目子课题。在Journal of the American Statistical Association, Annals of Statistics, Journal of Econometrics, Journal of Business & Economic Statistics，《经济学季刊》等国内国际知名学术期刊发表中论文40余篇。
Your participation is warmly welcomed!