<p>In network analysis, we often need to conduct statistical inference on the population network model using a single observed network via network statistics such as the largest eigenvalues of the adjacency matrix. However, since the sampling distributions of these network statistics are often complex, we rely on the bootstrap for such inference. In this article, we introduce a new bootstrap method for weighted networks to conduct statistical inference, focusing on the eigenvalues of the adjacency matrix as our statistic of interest. We establish desirable properties of the proposed method, such as bootstrap consistency. We demonstrate its applications in standard error estimation, confidence interval construction, and hypothesis testing, and show its superior performance in simulation and real data analysis.</p>

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Bootstrap-based statistical inference on the eigenvalues of weighted networks

  • Behzad Aalipur,
  • Yichen Qin

摘要

In network analysis, we often need to conduct statistical inference on the population network model using a single observed network via network statistics such as the largest eigenvalues of the adjacency matrix. However, since the sampling distributions of these network statistics are often complex, we rely on the bootstrap for such inference. In this article, we introduce a new bootstrap method for weighted networks to conduct statistical inference, focusing on the eigenvalues of the adjacency matrix as our statistic of interest. We establish desirable properties of the proposed method, such as bootstrap consistency. We demonstrate its applications in standard error estimation, confidence interval construction, and hypothesis testing, and show its superior performance in simulation and real data analysis.