Consistency and Asymptotic Normality of Stochastic Block Models\n Estimators from Sampled Data

2019/03/28 by Mahendra Mariadassou, Mariadassou, Mahendra, Timothée Tabouy +1
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Random Matrices and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1903.12488

openalex publication_date 2019/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Statistical analysis of network is an active research area and the literature\ncounts a lot of papers concerned with network models and statistical analysis\nof networks. However, very few papers deal with missing data in network\nanalysis and we reckon that, in practice, networks are often observed with\nmissing values. In this paper we focus on the Stochastic Block Model with\nvalued edges and consider a MCAR setting by assuming that every dyad (pair of\nnodes) is sampled identically and independently of the others with probability\n\ρ > 0. We prove that maximum likelihood estimators and its variational\napproximations are consistent and asymptotically normal in the presence of\nmissing data as soon as the sampling probability \ρ satisfies\n\ρ\≫\log(n)/n.\n

Citations

• Inference and missing data
• Modeling heterogeneity in random graphs through latent space models: a\n selective review
• On random graphs. I.

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