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2020 Consistency and asymptotic normality of stochastic block models estimators from sampled data
Mahendra Mariadassou, Timothée Tabouy
Electron. J. Statist. 14(2): 3672-3704 (2020). DOI: 10.1214/20-EJS1750

Abstract

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 $\rho \gg \log (n)/n$.

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Mahendra Mariadassou. Timothée Tabouy. "Consistency and asymptotic normality of stochastic block models estimators from sampled data." Electron. J. Statist. 14 (2) 3672 - 3704, 2020. https://doi.org/10.1214/20-EJS1750

Information

Received: 1 April 2019; Published: 2020
First available in Project Euclid: 6 October 2020

zbMATH: 07270274
MathSciNet: MR4159177
Digital Object Identifier: 10.1214/20-EJS1750

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Vol.14 • No. 2 • 2020
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