Uniform Inference for High-dimensional Quantile Regression: Linear Functionals and Regression Rank Scores

Understand

Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully.

• The theory of debiased estimators can be developed in the context of quantile regression models for a fixed quantile value.
• However, it is frequently desirable to formulate tests based on the quantile regression process, as this leads to more robust tests and more stable confidence sets.
• Additionally, inference in quantile regression requires estimation of the so called sparsity function, which depends on the unknown density of the error.