CONCENTRATION AND CONSISTENCY RESULTS FOR CANONICAL AND CURVED EXPONENTIAL-FAMILY MODELS OF RANDOM GRAPHS
CONCENTRATION AND CONSISTENCY RESULTS FOR CANONICAL AND CURVED EXPONENTIAL-FAMILY MODELS OF RANDOM GRAPHS
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DOI：
10.1214/19-aos1810
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发表时间：
2020-02-01
影响因子：
4.5
通讯作者：
Stewart, Jonathan
中科院分区：
文献类型：
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作者：
Schweinberger, Michael;Stewart, Jonathan
具有依赖边的随机图的指数族模型的统计推断是具有挑战性的。我们强调的重要性，额外的结构，并表明，额外的结构有利于统计推断。具有附加结构的随机图的一个简单例子是具有邻域和邻域内局部依赖的随机图。我们开发的第一个浓度和一致性结果的最大似然和M-估计的范围广泛的典型和弯曲的指数族模型的随机图的局部依赖。所有的结果都是非渐近的，适用于有限种群的随机图的节点，虽然渐近一致性的结果可以得到。此外，我们表明，额外的结构可以促进子图到图估计，并提出子图到图估计的浓度结果。作为应用，我们考虑了流行的随机图曲指数族模型，该模型具有由传递性和参数向量引起的局部依赖性，其维度取决于节点数量。
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and M-estimators of a wide range of canonical and curved exponential-family models of random graphs with local dependence. All results are nonasymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well. In addition, we show that additional structure can facilitate subgraph-to-graph estimation, and present concentration results for subgraph-to-graph estimators. As an application, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes.