The Annals of Statistics

The method of moments and degree distributions for network models

Peter J. Bickel, Aiyou Chen, and Elizaveta Levina

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Abstract

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average degree including Ω(1). Additional results are obtained for the important special case of degree distributions.

Article information

Source
Ann. Statist., Volume 39, Number 5 (2011), 2280-2301.

Dates
First available in Project Euclid: 11 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.aos/1321020525

Digital Object Identifier
doi:10.1214/11-AOS904

Mathematical Reviews number (MathSciNet)
MR2906868

Zentralblatt MATH identifier
1232.91577

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62G05: Estimation

Keywords
Social networks block model community detection

Citation

Bickel, Peter J.; Chen, Aiyou; Levina, Elizaveta. The method of moments and degree distributions for network models. Ann. Statist. 39 (2011), no. 5, 2280--2301. doi:10.1214/11-AOS904. https://projecteuclid.org/euclid.aos/1321020525


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