文章基本信息

标题：Consistency and asymptotic normality of stochastic block models estimators from sampled data
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作者：Mahendra Mariadassou ; Timothée Tabouy
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：2
页码：3672-3704
DOI：10.1214/20-EJS1750
语种：English
出版社：Institute of Mathematical Statistics
摘要：Statistical analysis of network is an active research area and the literature counts a lot of papers concerned with network models and statistical analysis of networks. However, very few papers deal with missing data in network analysis and we reckon that, in practice, networks are often observed with missing values. In this paper we focus on the Stochastic Block Model with valued edges and consider a MCAR setting by assuming that every dyad (pair of nodes) is sampled identically and independently of the others with probability $\rho >0$. We prove that maximum likelihood estimators and its variational approximations are consistent and asymptotically normal in the presence of missing data as soon as the sampling probability $\rho $ satisfies $\rho \gg \log (n)/n$.
关键词：Stochastic Block Model;Missing data;Asymptotic normality;Maximum likelihood;Concentration inequality