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December 2015 Subsampling bootstrap of count features of networks
Sharmodeep Bhattacharyya, Peter J. Bickel
Ann. Statist. 43(6): 2384-2411 (December 2015). DOI: 10.1214/15-AOS1338

Abstract

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.

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Sharmodeep Bhattacharyya. Peter J. Bickel. "Subsampling bootstrap of count features of networks." Ann. Statist. 43 (6) 2384 - 2411, December 2015. https://doi.org/10.1214/15-AOS1338

Information

Received: 1 February 2014; Revised: 1 April 2015; Published: December 2015
First available in Project Euclid: 7 October 2015

zbMATH: 1326.62067
MathSciNet: MR3405598
Digital Object Identifier: 10.1214/15-AOS1338

Subjects:
Primary: 62F40 , 62G09
Secondary: 62D05

Keywords: bootstrap , count features , model-based sampling , networks , subsampling

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December 2015
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