Statistical Inference for Interactions and Infinite-Dimensional Estimands

Abstract

In this dissertation, we make methodological contributions to three statistical inference problems. We first consider two challenges that can arise when assessing for interactions, and we then discuss inference for complex estimands in semiparametric and nonparametric models. In Chapter 2, we propose an inferential procedure for identifying when an effect is substantially stronger in some sub-populations than in others. In Chapter 3, we propose a method for differential network analysis in the setting where the dependencies shared among the nodes are associated with covariates. In Chapter 4, we introduce an approach to inference on infinite-dimensional estimands that does not require the estimand of interest to take a parametric form. We conclude with a summary and a discussion of potential future research directions in Chapter 5.