Design-based Estimation and Inference on Quantile Exposure Effect under General Interference

Abstract

Many applications in public health, environmental science, and economics feature spillovers across connected units, violating the Stable Unit Treatment Value Assumption (SUTVA) underlying classical quantile treatment effect methods. We develop a general framework for defining, estimating, and conducting inference for quantile exposure effects (QEEs) under network interference, encompassing quantile direct and spillover effects as leading cases. Studying QEEs under interference faces three substantive challenges. First, because a single exposure level represents many neighborhood treatment configurations, the causal estimand must aggregate over these configurations in an interpretable manner. Second, quantile estimands are intrinsically non-smooth, placing them outside much of the existing network theory involving only Lipschitz or differentiable functionals. Third, in design-based, finite-population network settings, conventional smoothness assumptions on outcome densities cannot be imposed directly. Using conditional neighborhood dependence, we establish asymptotic normality under explicit network degree conditions and derive a locally uniform convergence rate for kernel density estimation. We also characterize the variance estimation bias arising from heterogeneous unit-specific score means and construct asymptotically conservative confidence intervals. Extensive simulations and an application to an educational intervention in school friendship networks demonstrate that the proposed framework reveals heterogeneous exposure effects, including tail-specific impacts, that are missed by analyses based solely on average treatment effects.