Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models

Understand

This work proposes new inference methods for a regression coefficient of interest in a (heterogeneous) quantile regression model.

• We consider a high-dimensional model where the number of regressors potentially exceeds the sample size but a subset of them suffice to construct a reasonable approximation to the conditional quantile function.
• The proposed methods are (explicitly or implicitly) based on orthogonal score functions that protect against moderate model selection mistakes, which are often inevitable in the approximately sparse model considered in the present paper.
• We establish the uniform validity of the proposed confidence regions for the quantile regression coefficient.