ASYMPTOTICS IN DIRECTED EXPONENTIAL RANDOM GRAPH MODELS WITH AN INCREASING BI-DEGREE SEQUENCE

• 成果类型: Article
• 署名作者: Yan, Ting; Leng, Chenlei; Zhu, Ji
• 署名单位: Central China Normal University; University of Warwick; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1343
• 发表日期: 2016
• 页码: 31-57
• 关键词: p-asterisk models; PROBABILITY-DISTRIBUTIONS; expotential family; network; Consistency; number; normality; THEOREM

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 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 as well as continuous weighted edges. We establish the uniform consistency and the asymptotic normality for the maximum likelihood estimate, 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. Numerical studies confirm our theoretical findings.