The Annals of Statistics

Subsampling bootstrap of count features of networks

Sharmodeep Bhattacharyya and Peter J. Bickel

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Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is still underway. We propose bootstrap subsampling methods for finding empirical distribution of count features or “moments” (Bickel, Chen and Levina [Ann. Statist. 39 (2011) 2280–2301]) and smooth functions of these features for the networks. Using these methods, we cannot only estimate the variance of count features but also get good estimates of such feature counts, which are usually expensive to compute numerically in large networks. In our paper, we prove theoretical properties of the bootstrap estimates of variance of the count features as well as show their efficacy through simulation. We also use the method on some real network data for estimation of variance and expectation of some count features.

Article information

Ann. Statist., Volume 43, Number 6 (2015), 2384-2411.

Received: February 2014
Revised: April 2015
First available in Project Euclid: 7 October 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F40: Bootstrap, jackknife and other resampling methods 62G09: Resampling methods
Secondary: 62D05: Sampling theory, sample surveys

Networks subsampling bootstrap count features model-based sampling


Bhattacharyya, Sharmodeep; Bickel, Peter J. Subsampling bootstrap of count features of networks. Ann. Statist. 43 (2015), no. 6, 2384--2411. doi:10.1214/15-AOS1338.

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Supplemental materials

  • Supplement to “Subsampling bootstrap of count features of networks”. In the Supplement, we prove Theorems 1, 2, Proposition 6, Lemmas 7 and 8.