Primary Submission Category: Heterogeneous Treatment Effects
Uniform Inference for Local Conditional Quantile Treatment Effect Curve with High-Dimensional Covariates
Authors: Jing Tao,
Presenting Author: Jing Tao*
In this study, we investigate heterogeneous local quantile treatment effects for observational data with high-dimensional covariates without relying on the strong ignorability assumption. Using a binary instrumental variable, the parameters of interest are in a population subgroup (compliers) through a two-stage regression model. We develop Lasso estimation with a non-convex and non-smooth objective function to estimate the parameters of interest. We propose a de-sparsifying estimator for pointwise and uniform inference for quantile treatment effects. Moreover, we obtain uniform strong approximations of the local quantile treatment process by conditionally pivotal and Gaussian processes. Based on these strong approximations, we develop bootstrap resampling methods to construct uniform confidence bands for the heterogeneous/conditional local quantile treatment effects given high-dimensional covariates. Finally, we evaluate performance through simulation studies.