Open Access
August 2019 Dynamic network models and graphon estimation
Marianna Pensky
Ann. Statist. 47(4): 2378-2403 (August 2019). DOI: 10.1214/18-AOS1751


In the present paper, we consider a dynamic stochastic network model. The objective is estimation of the tensor of connection probabilities $\mathbf{{\Lambda}}$ when it is generated by a Dynamic Stochastic Block Model (DSBM) or a dynamic graphon. In particular, in the context of the DSBM, we derive a penalized least squares estimator $\widehat{\boldsymbol{\Lambda}}$ of $\mathbf{{\Lambda}}$ and show that $\widehat{\boldsymbol{\Lambda}}$ satisfies an oracle inequality and also attains minimax lower bounds for the risk. We extend those results to estimation of $\mathbf{{\Lambda}}$ when it is generated by a dynamic graphon function. The estimators constructed in the paper are adaptive to the unknown number of blocks in the context of the DSBM or to the smoothness of the graphon function. The technique relies on the vectorization of the model and leads to much simpler mathematical arguments than the ones used previously in the stationary set up. In addition, all results in the paper are nonasymptotic and allow a variety of extensions.


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Marianna Pensky. "Dynamic network models and graphon estimation." Ann. Statist. 47 (4) 2378 - 2403, August 2019.


Received: 1 April 2017; Revised: 1 March 2018; Published: August 2019
First available in Project Euclid: 21 May 2019

zbMATH: 07082290
MathSciNet: MR3953455
Digital Object Identifier: 10.1214/18-AOS1751

Primary: 60G05
Secondary: 05C80 , 62F35

Keywords: dynamic network , graphon , Minimax rate , Nonparametric regression , Stochastic block model

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.47 • No. 4 • August 2019
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