Local Bootstrap for Network Data

IF 2.4 2区 数学 Q2 BIOLOGY
Biometrika Pub Date : 2024-09-09 DOI:10.1093/biomet/asae046
Tianhai Zu, Yichen Qin
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引用次数: 0

Abstract

SUMMARY In network analysis, we frequently need to conduct inference for network parameters based on one observed network. Since the sampling distribution of the statistic is often unknown, we need to rely on the bootstrap. However, due to the complex dependence structure among vertices, existing bootstrap methods often yield unsatisfactory performance, especially under small or moderate sample sizes. To this end, we propose a new network bootstrap procedure, termed local bootstrap, to estimate the standard errors of network statistics. We propose to resample the observed vertices along with their neighbor sets, and reconstruct the edges between the resampled vertices by drawing from the set of edges connecting their neighbor sets. We justify the proposed method theoretically with desirable asymptotic properties for statistics such as motif density, and demonstrate its excellent numerical performance in small and moderate sample sizes. Our method includes several existing methods, such as the empirical graphon bootstrap, as special cases. We investigate the advantages of the proposed methods over the existing methods through the lens of edge randomness, vertex heterogeneity, neighbor set size, which shed some light on the complex issue of network bootstrapping.
网络数据的本地引导
摘要 在网络分析中,我们经常需要根据一个观测网络来推断网络参数。由于统计量的抽样分布往往是未知的,因此我们需要依靠自举法。然而,由于顶点之间存在复杂的依赖结构,现有的自举方法往往效果不佳,尤其是在样本量较小或中等的情况下。为此,我们提出了一种新的网络引导程序,称为局部引导,用于估计网络统计的标准误差。我们建议对观察到的顶点及其邻居集进行重新采样,并从连接其邻居集的边缘集中抽取,重建重新采样顶点之间的边缘。我们从理论上证明了所提议的方法对图案密度等统计数据具有理想的渐近特性,并证明了该方法在中小规模样本中的优异数值性能。我们的方法包括几种现有方法,如经验图引导法,作为特例。我们从边缘随机性、顶点异质性、邻居集大小等角度研究了所提方法相对于现有方法的优势,从而揭示了网络引导这一复杂问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biometrika
Biometrika 生物-生物学
CiteScore
5.50
自引率
3.70%
发文量
56
审稿时长
6-12 weeks
期刊介绍: Biometrika is primarily a journal of statistics in which emphasis is placed on papers containing original theoretical contributions of direct or potential value in applications. From time to time, papers in bordering fields are also published.
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