Inference and uncertainty characterization in complex structures

The common theme of the projects in this thesis is statistical inference and characterizing uncertainty for complex structures, including networks and separately exchangeable data matrices. In the first two projects, we focus on uncertainty quantification of network subgraph count statistics. In the first project, we study the network jackknife procedure to consistently estimate the variance of subgraph counts under the sparse graphon model. In the second project, we develop a family of network multiplier bootstraps for subgraph counts using linear and quadratic weights. In both projects, we complement our theoretical proofs with simulation studies and real data analysis on social networks. In the final third project we consider the more elementary questions of how investigators arrive at certain model assumptions, focusing on commonly used symmetry assumptions known as various forms of exchangeability. In particular, we argue for a more common use of separate exchangeability as a modeling principle. We show how this notion is still ignored in some recent work, but could easily be included.