Higher-Order Correct Multiplier Bootstraps for Count Functionals of Networks
Higher-Order Correct Multiplier Bootstraps for Count Functionals of Networks
复制标题
网络计数泛函的高阶正确乘法器自举
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Purnamrita Sarkar
中科院分区：
文献类型：
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作者：
Qiaohui Lin;Robert Lunde;Purnamrita Sarkar
子图计数在图极限理论和网络数据分析中都起着核心作用。近年来，这些泛函的不确定性量化领域取得了实质性进展；现在已知有几个程序对于该问题是一致的。在本文中，我们提出了一类新的计数泛函乘法器引导程序。我们证明，具有乘法权重的引导程序在适当的稀疏条件下表现出高阶正确性。由于该引导程序的计算成本很高，因此我们提出了乘法器引导程序的线性和二次近似，它们分别对应于近似 U 统计量的一阶和二阶哈耶克投影。我们证明，二次引导程序在与乘法引导程序类似的条件下实现了更高阶的正确性，同时具有更好的计算特性。我们通过模拟研究补充了我们的理论结果，并验证了我们的程序为多个函数提供了最先进的性能。
Subgraph counts play a central role in both graph limit theory and network data analysis. In recent years, substantial progress has been made in the area of uncertainty quantification for these functionals; several procedures are now known to be consistent for the problem. In this paper, we propose a new class of multiplier bootstraps for count functionals. We show that a bootstrap procedure with a multiplicative weights exhibits higher-order correctness under appropriate sparsity conditions. Since this bootstrap is computationally expensive, we propose linear and quadratic approximations to the multiplier bootstrap, which correspond to the first and second-order Hayek projections of an approximating U-statistic, respectively. We show that the quadratic bootstrap procedure achieves higher-order correctness under analogous conditions to the multiplicative bootstrap while having much better computational properties. We complement our theoretical results with a simulation study and verify that our procedure offers state-of-the-art performance for several functionals.
网络分析中的极小极大率：图估计、社区检测和假设检验
影响因子：
5.7
作者：
Gao, Chao;Ma, Zongming
通讯作者：
Ma, Zongming