Leveraging Graph Structure for Optimal Design, Estimation, and Inference under Interference

Abstract

Many systems of scientific interest are composed of interacting and interdependent units.In such settings, observations cannot generally be treated as independent, and in experiments, one unit's treatment assignment may affect the outcomes of other units through interference. This dissertation studies inference, testing, estimation, and experimental design in these dependent-data settings, with a particular focus on leveraging network structure. First, I develop general covariance-based sufficient conditions for multivariate central limit theorems withdependent triangular arrays. The framework allows nonzero dependence between all observations and I show how it encompasses several commonly studied dependence structures. Second, I study conditional randomization tests for detecting network interference by conditioning on focal units, deriving power characterizations that motivate optimization-based focal-unit selection. Third, I consider treatment-effect estimation when the correct exposure threshold is unknown. I propose a data-adaptive procedure that estimates the bias--variance trade-off across candidate exposure thresholds and selects the threshold minimizing estimated mean squared error. Finally, I study optimal experimental design under network interference, homophily, and heterogeneous variation. I derive worst-case mean-squared-error bounds that lead to an optimization over the covariance matrix of the treatment assignment, and develop design procedures based on semidefinite programming with Gaussian rounding and vector balancing via the Gram--Schmidt Walk. Together, these results study how dependence structure can be used at different stages ofstatistical analysis: to justify inference, improve detection of interference, adapt treatment-effect estimators, and construct optimal experimental designs.