A1212
Title: Regression discontinuity designs for random objects
Authors: Daisuke Kurisu - The University of Tokyo (Japan) [presenting]
Yidong Zhou - University of California, Davis (United States)
Taisuke Otsu - London School of Economics (United Kingdom)
Hans-Georg Mueller - University of California Davis (United States)
Abstract: A generalization of regression discontinuity designs is proposed to handle random objects residing in geodesic metric spaces. A key challenge in this setting is the absence of algebraic operations, which makes it difficult to define treatment effects using simple differences. To address this, the causal effect at the cutoff is defined as a geodesic between the local Frechet means of untreated and treated outcomes. Estimation is carried out using local Frechet regression. The proposed geodesic regression discontinuity design method is supported by theory, including convergence rate guarantees, and is demonstrated in applications where causal inference is of interest in complex outcome spaces.
