Testing High-Dimensional Effects in Quantile Regression with High-Dimensional Confounding: A Decorrelated Approach

This paper addresses the challenge of testing high-dimensional coefficients in quantile regression in the presence of high-dimensional nuisance parameters. We first extend a recently proposed score test by incorporating a convolution-type smoothed quantile loss, which facilitates efficient computation and scalable inference.

We derive the asymptotic distributions of the resulting smoothing score test under both the null and local alternatives, assuming weak correlations between variables of interest and potential confounders. To mitigate the bias caused by strong correlations, we further develop a decorrelated version that improves both Type-I error control and power. Theoretical properties, including the limiting null distribution and power behavior, are established in settings where both the target and nuisance parameters are ultrahigh-dimensional.