Primary Submission Category: Heterogeneous Treatment Effects
The Parachute Hybrid CATE Estimator and Bootstrap Methods: Theory and Applications
Authors: Xianlin Sun, Stephen Man Sing Lee,
Presenting Author: Xianlin Sun*
We propose a parachute hybrid estimator of the conditional average treatment effect (CATE) under the potential outcome framework. Itis a fully robust approach combining parametric (Meng and Qiao 2022) and nonparametric (Abrevaya, Hsu, and Lieli 2015) methods using the hybrid mechanism of Lee and Soleymani (2015) to estimate CATE. The key innovation is “graceful degradation”: when at least one of the propensity score or outcome models is correctly specified, it achieves parametric convergence rates—the defining property of double robustness. When both are misspecified, it remains consistent, with convergencedegraded to nonparametric rates—hence “parachute.” Its asymptotic distribution is derived by adopting M-estimation (Stefanski and Boos 2002) and incorporating Lyapunov’s Central Limit Theorem.
Bootstrap-based methods for statistical inference overcome plug-in variance estimation challenges. We prove that the generalized bootstrap method provides a consistent estimator for the distribution of the parachute hybrid estimator under general assumptions, grounded in Chatterjee and Bose (2005).