报告人：晏挺
报告地点：数学与统计学院五楼科学报告厅（501室）
报告时间：2015年12月10日星期四09:45-10:30
主讲人简介：
晏挺，华中师范大学统计系副教授，2012年毕业于中国科学技术大学，获博士学位，2013年获美国乔治华盛顿大学统计系博士后。研究兴趣主要包括：（社交，经济，生物等）网络模型；随机图； 成对比较；基因型数据的统计分析。
报告摘要：
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study the statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary and non-binary weighted edges. We establish the uniform consistency and the asymptotic normality of the maximum likelihood estimator, when the number of parameters grows and only one realized observation of the graph is available. One key technique in the proofs is to approximate the inverse of the Fisher information matrix using a simple matrix with high accuracy. Along the way, we also establish a geometrically fast rate of convergence for the Newton iterative algorithm, which is used to obtain the maximum likelihood estimate. Numerical studies confirm our theoretical findings.
