Testing for Differences in Stochastic Network Structure
提出两种基于算子范数的随机化检验，用于判断两个网络是否来自同一随机图模型，尤其适用于经济学中常见的稀疏和度异质网络。
How can one determine whether a treatment, such as the introduction of a social program or trade shock, alters agents' incentives to form links in a network? This paper proposes analogs of a two‐sample Kolmogorov–Smirnov test, widely used in the literature to test the null hypothesis of no treatment effects, for network data. It first specifies a testing problem in which the null hypothesis is that two networks are drawn from the same random graph model. It then describes two randomization tests based on the magnitude of the difference between the networks' adjacency matrices as measured by the 2 → 2 and ∞ → 1 operator norms. Power properties of the tests are examined analytically, in simulation, and through two real‐world applications. A key finding is that the test based on the ∞ → 1 norm can be much more powerful for the kinds of sparse and degree‐heterogeneous networks common in economics.