Subsampling sparse graphons under minimal assumptions

• 成果类型: Article
• 署名作者: Lunde, Robert; Sarkar, Purnamrita
• 署名单位: University of Michigan System; University of Michigan; University of Texas System; University of Texas Austin
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac032
• 发表日期: 2023
• 页码: 1532
• 关键词: Community Detection; counting triangles; models; bootstrap; LIMITS

摘要

We study the properties of two subsampling procedures for networks, vertex subsampling and p-subsampling, under the sparse graphon model. The consistency of network subsampling is demonstrated under the minimal assumptions of weak convergence of the corresponding network statistics and an expected subsample size growing to infinity more slowly than the number of vertices in the network. Furthermore, under appropriate sparsity conditions, we derive limiting distributions for the nonzero eigenvalues of an adjacency matrix under the sparse graphon model. Our weak convergence result implies the consistency of our subsampling procedures for eigenvalues under appropriate conditions.