报告人：兰伟
报告地点：腾讯会议ID:793-996-450
报告时间：2022年10月20日星期四15:00-16:00
报告摘要：
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 (see, e.g., Lei 2016 and Hu et al. 2021). 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 $O(n^{-1}\log n)$. To fill this gap, we propose a novel goodness-of-fit test for the stochastic block model. The key idea is combining the test concept from Hu et al. (2021) with a sampling process that alleviates the negative impacts of network sparsity. 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 sparse and dense networks indicate that the proposed method performs well.
主讲人简介：
兰伟，博士毕业于北京大学光华管理学院，现为西南财经大学统计学院副院长，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。担任国际统计学期刊《STAT》副主编，在Journal of the American Statistical Association, Annals of Statistics, Journal of Econometrics, Journal of Business & Economic Statistics，《中国科学》、《统计研究》等国内国际知名统计学期刊发表中英文论文40多篇。
