Network data is a major object data type that has been widely collected or derived from common sources such as brain imaging. Such data contains numeric, topological, and geometrical information, and may be necessarily considered in certain non-Euclidean space for appropriate statistical analysis. The development of statistical methodologies for network data is challenging and currently at its infancy; for instance, the non-Euclidean counterpart of basic two-sample tests for network data is scarce in literature. In this study, a novel framework is presented for two independent sample comparison of networks. Specifically, an approximation distance metric to quotient Euclidean distance is proposed, and then combined with network spectral distance to quantify the local and global dissimilarity of networks simultaneously. A permutational non-Euclidean analysis of variance is adapted to the proposed distance metric for the comparison of two independent groups of networks. Comprehensive simulation studies and real applications are conducted to demonstrate the superior performance of our method over other alternatives. The asymptotic properties of the proposed test are investigated and its high-dimensional extension is discussed as well.
翻译:网络数据是广泛收集或从脑成像等共同来源获得的主要对象数据类型,这些数据包含数字、地形学和几何信息,可能在某些非欧化空间中予以考虑,以便进行适当的统计分析。为网络数据制定统计方法具有挑战性,目前尚处于初级阶段;例如,文献中缺乏关于网络数据基本两样抽样测试的非欧化对等方。在这项研究中,为两个独立的网络抽样比较提出了一个新框架。具体地说,提议了一个与欧几里德距离相比的近似距离指标,然后与网络光谱距离相结合,同时量化网络的本地和全球差异性。对差异进行的非欧化非欧化分析适应了拟议的距离指标,以比较两个独立的网络组。进行了全面模拟研究和实际应用,以证明我们的方法优于其他替代方法的优异性。对拟议测试的微量特征进行了调查,并讨论了高维度扩展。