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Estimation of on- and off-time distributions in a dynamic Erdős–Rényi random graph

Part of: Inference from stochastic processes Parametric inference Graph theory

Published online by Cambridge University Press:  09 October 2025

Michel R. H. Mandjes  and
Jiesen Wang Open the ORCID record for Jiesen Wang [Opens in a new window]
Michel R. H. Mandjes*
Affiliation:
Leiden University ; University of Amsterdam
Jiesen Wang*
Affiliation:
University of Amsterdam
*
*Postal address: Mathematical Institute, Leiden University, P.O. Box 9512, 2300, RA Leiden, The Netherlands. Email: m.r.h.mandjes@math.leidenuniv.nl
***Postal address: University of Amsterdam, Science Park 107, 1098 XG Amsterdam, The Netherlands. Email: jiesenwang@gmail.com
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Abstract

In this paper we consider a dynamic Erdős–Rényi graph in which edges, according to an alternating renewal process, change from present to absent and vice versa. The objective is to estimate the on- and off-time distributions while only observing the aggregate number of edges. This inverse problem is dealt with, in a parametric context, by setting up an estimator based on the method of moments. We provide conditions under which the estimator is asymptotically normal, and we point out how the corresponding covariance matrix can be identified. We also demonstrate how to adapt the estimation procedure if alternative subgraph counts are observed, such as the number of wedges or triangles.

Keywords

Dynamic random graphspartial informationinverse problemparametric inferencemethod of moments

MSC classification

Primary: 05C80: Random graphs
Secondary: 62M09: Non-Markovian processes 62F12: Asymptotic properties of estimators

Information

Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 30
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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