SUBSAMPLING BOOTSTRAP OF COUNT FEATURES OF NETWORKS

• 成果类型: Article
• 署名作者: Bhattacharyya, Sharmodeep; Bickel, Peter J.
• 署名单位: University of California System; University of California Berkeley; Oregon State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1338
• 发表日期: 2015
• 页码: 2384-2411
• 关键词: motifs

摘要

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.