A1129
Title: Rates of convergence and normal approximations for estimators of local dependence random graph models
Authors: Jonathan Stewart - Florida State University (United States) [presenting]
Abstract: 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 a prior study, research in the statistical network analysis and network science literature has demonstrated the potential and utility of this class of models. The first statistical disclaimers are provided, 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, the first non-asymptotic bounds are derived on the L2 error of maximum likelihood estimators, along with convergence rates, outlining conditions under which these rates are minimax optimal. Second, and more importantly, the first non-asymptotic bounds are derived on the error of the multivariate normal approximation. Together, the developed theoretical results are the first set of conditions which achieve both optimal rates of convergence and non-asymptotic bounds on the error of the multivariate normal approximation for local dependence random graph models.
