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

原文摘要

Quantile regression provides a flexible framework in econometrics for modeling the relationship between a response variable and multivariate predictors, particularly when heterogeneous effects are present. 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. Comprehensive simulation results validate our theory and demonstrate the robustness and effectiveness of the proposed test when dealing with heavy-tailed and asymmetric data. We further illustrate the practical utility of our method through an empirical analysis of U.S. stock market data. Software implementing the methodology is available in the R package TestSQR.

摘要来源：OpenAlex