Causal Rank Lasso for Single Index Model

Abstract

This letter focuses on estimating the average treatment effect within a high-dimensional single-index model framework. We employ the recently introduced concept of the rank average treatment effect (rank-ATE) as an alternative measure for assessing differences in potential outcomes. To estimate both the rank-ATE and the model parameters simultaneously, we propose the causal rank Lasso estimator. Specifically, our method involves regressing the outcome rank on both the the treatment indicator and the covariates. We demonstrate that our estimator consistently identifies the direction and support of the true model parameter. Additionally, we introduced a novel irrepresentable condition to establish the support recovery in causal rank Lasso. Simulation studies are provided to validate the efficacy of our approach.