Deep Orthogonal Learner for Conditional Quantile Treatment Effect Estimation

In recent years, orthogonal statistical learning has been widely recognized for its ability to reduce sensitivity with respect to nuisance parameters to estimate the target parameter, making it an important tool in causal inference, particularly in the estimation of the conditional average treatment effect (CATE). However, its application on conditional quantile treatment effect (CQTE), which offers a more comprehensive perspective on treatment effects than CATE, has not yet been explored comprehensively. In this article, we propose a novel method for learning CQTE. This method shares Neyman-orthogonal property, which produces CQTE estimators that are insensitive to small perturbations of nuisance functions. We first model the CQTE nonparametrically and use deep learning to estimate it. We establish the convergence rate of the neural network estimator, demonstrating that it achieves the minimax optimal rate of convergence (up to a polylogarithmic factor). This highlights deep learning’s ability to identify low-dimensional structures in high-dimensional data. Additionally, we then model CQTE linearly to facilitate interpretation and statistical inference. We prove that the corresponding coefficient and CQTE estimators achieve root-n consistency and asymptotic normality, even if the estimators of the nuisance parameters converge at a slower rate. Through empirical evaluation for numerical studies, we demonstrate the superiority of our method compared to competing methods.