Local dependence random graph models are a class of block models for network data which allow for dependence among edges under a local dependence assumption defined around the block structure of the network. Since being introduced by Schweinberger and Handcock (2015), research in the statistical network analysis and network science literatures have demonstrated the potential and utility of this class of models. In this work, we provide the first statistical disclaimers which provide conditions under which estimation and inference procedures can be expected to provide accurate and valid inferences. This is accomplished by deriving convergence rates of inference procedures for local dependence random graph models based on a single observation of the graph, allowing both the number of model parameters and the sizes of blocks to tend to infinity. First, we derive the first non-asymptotic bounds on the $\ell_2$-error of maximum likelihood estimators, along with convergence rates. Second, and more importantly, we derive the first non-asymptotic bounds on the error of the multivariate normal approximation. In so doing, we introduce the first principled approach to providing statistical disclaimers through quantifying the uncertainty about statistical conclusions based on data.

翻译：局部依赖随机图模型是一类用于网络数据的块模型，该模型在围绕网络块结构定义的局部依赖假设下允许边之间存在依赖关系。自Schweinberger和Handcock（2015）提出以来，统计网络分析与网络科学领域的研究已证明了这类模型的潜力与实用性。本文首次提供了统计免责声明，给出了估计与推断过程能够产生准确且有效推断的条件。我们通过推导基于单次图观测的局部依赖随机图模型推断过程的收敛速度来实现这一目标，允许模型参数数量与块大小趋于无穷。首先，我们推导出最大似然估计量在$\ell_2$误差上的首个非渐近界及其收敛速度。其次，更重要的是，我们推导出多元正态近似误差的首个非渐近界。在此过程中，我们引入了首个通过量化数据统计结论不确定性来提供统计免责声明的原则性方法。