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.

翻译：我们开发了一系列方法，用于调整分位数回归的预测以确保覆盖性。这些方法具有模型无关性，可在仅需最小假设条件下校正高维过拟合偏差。理论结果表明，我们所构建的估计量具有一致性，并在比例渐近框架下（数据维度与样本量之比收敛于常数）实现了精确校准。模拟数据与真实数据的实验进一步验证了该结论。本工作的核心创新在于建立了留一法覆盖性与分位数回归对偶形式中变量拟合值之间的新关联，这显著降低了多种场景下交叉验证的计算成本。