Correcting the Coverage Bias of Quantile Regression

TL;DR

This paper introduces model-agnostic methods to correct coverage bias in quantile regression, ensuring accurate calibration and reducing computational costs through a novel leave-one-out approach.

Contribution

It presents new techniques for coverage correction in quantile regression that are theoretically consistent and computationally efficient, applicable in high-dimensional settings.

Findings

Methods achieve consistent coverage correction.

Experimental validation on simulated and real data.

Reduced computational costs via a new leave-one-out approach.

Abstract

We develop a collection of methods for adjusting the predictions of quantile regression to ensure coverage. Our methods are model agnostic and can be used to correct for high-dimensional overfitting bias with only minimal assumptions. Theoretical results show that the estimates we develop are consistent and facilitate accurate calibration in the proportional asymptotic regime where the ratio of the dimension of the data and the sample size converges to a constant. This is further confirmed by experiments on both simulated and real data. A key component of our work is a new connection between the leave-one-out coverage and the fitted values of variables appearing in a dual formulation of the quantile regression problem. This facilitates the use of cross-validation in a variety of settings at significantly reduced computational costs.