标题： 无需假设的网络关联数据推断 显示英文标题

标题： Assumption-lean Inference for Network-linked Data

摘要： 我们考虑网络关联回归问题的统计推断，其中协变量可能包括为每个节点计算的网络摘要统计量。在涉及网络数据的情况下，通常假设潜在变量决定了图中的连接概率。由于这些潜在特征的存在使得经典回归假设更加不可靠，我们提出了一个假设较少的框架，用于联合可交换回归数组的线性回归。我们建立了此类数组的Aldous-Hoover表示的类似形式，这可能具有独立的兴趣。此外，我们考虑了两种不同的投影参数作为潜在目标，并建立了当常用网络统计量（包括局部子图频率和谱嵌入）作为协变量时，渐近正态性和自助一致性成立的条件。在使用局部计数统计量的线性回归情况下，我们表明，偏差校正估计量允许在比OLS估计量更弱的稀疏条件下针对更自然的推断目标。我们的推断工具通过模拟数据和与小学学术环境相关的实际数据进行了说明。 显示英文摘要

摘要： We consider statistical inference for network-linked regression problems, where covariates may include network summary statistics computed for each node. In settings involving network data, it is often natural to posit that latent variables govern connection probabilities in the graph. Since the presence of these latent features makes classical regression assumptions even less tenable, we propose an assumption-lean framework for linear regression with jointly exchangeable regression arrays. We establish an analog of the Aldous-Hoover representation for such arrays, which may be of independent interest. Moreover, we consider two different projection parameters as potential targets and establish conditions under which asymptotic normality and bootstrap consistency hold when commonly used network statistics, including local subgraph frequencies and spectral embeddings, are used as covariates. In the case of linear regression with local count statistics, we show that a bias-corrected estimator allows one to target a more natural inferential target under weaker sparsity conditions compared to the OLS estimator. Our inferential tools are illustrated using both simulated data and real data related to the academic climate of elementary schools.