THE METHOD OF MOMENTS AND DEGREE DISTRIBUTIONS FOR NETWORK MODELS

• 成果类型: Article
• 署名作者: Bickel, Peter J.; Chen, Aiyou; Levina, Elizaveta
• 署名单位: University of California System; University of California Berkeley; Alphabet Inc.; Google Incorporated; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS904
• 发表日期: 2011
• 页码: 2280-2301
• 关键词: stochastic blockmodels; prediction

摘要

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average degree including Omega (1). Additional results are obtained for the important special case of degree distributions.