Primary Submission Category: Heterogeneous Treatment Effects
The Parachuted Hybrid CATE Estimator with Bootstrap Methods for Inference
Authors: Xianlin Sun, Stephen Man Sing Lee,
Presenting Author: Xianlin Sun*
This paper introduces a novel hybrid estimator for the Conditional Average Treatment Effect (CATE) that achieves optimal convergence rates and robustness against model mis-specification. Our proposed “parachute” estimator exhibits the oracle property: it achieves the fast parametric convergence rate when either the propensity score or outcome model is correctly specified, and gracefully degrades to the slower non-parametric rate when both are mis-specified. We make two primary contributions.
First, we derive the complete asymptotic distribution of the joint vector of parametric and non-parametric CATE estimators. This theoretical novelty culminates in Theorem 1, establishing their joint asymptotic normality. Corollary 1 characterizes the asymptotic distribution of our hybrid estimator, revealing its adaptive “parachute” mechanism. The complexity of this distribution motivates our second contribution.
Second, we establish the theoretical validity of bootstrap methods for constructing confidence intervals. Theorem 2 proves the consistency of the bootstrap for estimating the hybrid estimator’s distribution, providing a practical tool for statistical inference. This builds upon Chatterjee and Bose’s (2005) framework for M-estimation. Detailed proofs are in the Appendix. We conclude with a simulation study demonstrating our estimator’s empirical performance and bootstrap coverage properties.