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Subsampling bootstrap of count features of networks

机译：网络数量特征的支持自动启动

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摘要

The emergence of a huge number of network data sets creates a need for appropriate statistical analysis and interpretation. Information networks have arisen in connection with text mining and also technological networks such as the Internet have become objects of study. In this article, a nonparametric formulation for network models where node labels carry no information is considered. Subsampling-based bootstrap approaches are used to estimate count statistics and to obtain approximate distributions for such count statistics. The bootstrap subsampling methods and the theoretical properties of each bootstrap estimator are presented in detail. Several examples where the use of count statistics provides useful insights into the behavior of the networks are given. A method for estimating asymptotic variances of these estimators using bootstrap is discussed and a theoretical comparison of the methods is considered. The general theorem on asymptotic Gaussianity of bootstrap subsampling estimates of count statistics and their variance is presented. The theoretical properties of the bootstrap estimates of variance of the count features as well as their efficacy are proven through a simulation. The proposed method is also used on some real network data for estimation of variance and expectation of some count features.
机译：大量网络数据集的出现需要进行适当的统计分析和解释。与文本挖掘相关的信息网络已经出现，互联网等技术网络也已成为研究对象。在本文中，考虑了节点标签不携带任何信息的网络模型的非参数公式。基于子抽样的bootstrap方法用于估计计数统计，并获得此类计数统计的近似分布。详细介绍了bootstrap子抽样方法和每个bootstrap估计器的理论性质。文中给出了使用计数统计数据对网络行为提供有用见解的几个例子。讨论了用bootstrap估计这些估计量的渐近方差的方法，并对这些方法进行了理论比较。给出了计数统计量及其方差的bootstrap次抽样估计的渐近高斯性的一般定理。通过仿真验证了计数特征方差bootstrap估计的理论性质及其有效性。该方法还用于一些实际网络数据，以估计某些计数特征的方差和期望值。

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