We propose a robust method for constructing conditionally valid prediction intervals based on models for conditional distributions such as quantile and distribution regression. Our approach can be applied to important prediction problems including cross-sectional prediction, k-step-ahead forecasts, synthetic controls and counterfactual prediction, and individual treatment effects prediction. Our method exploits the probability integral transform and relies on permuting estimated ranks. Unlike regression residuals, ranks are independent of the predictors, allowing us to construct conditionally valid prediction intervals under heteroskedasticity. We establish approximate conditional validity under consistent estimation and provide approximate unconditional validity under model misspecification, overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.

翻译：我们建议了一种稳健的方法,用于根据量化和分布回归等有条件分布模型构建有条件有效预测间隔。我们的方法可以适用于重要的预测问题,包括跨部门预测、K步头预测、合成控制和反事实预测以及个人治疗效应预测。我们的方法利用概率整体变换,并依赖各种估计等级。与回归残留值不同,等级与预测值不同,允许我们在四重心状态下构建有条件有效预测间隔。我们根据一致的估计设定了大致的有条件有效性,并根据模型的错误区分、超配和时间序列数据提供近似无条件的有效性。我们还提议对基线方法进行简单的“形状”调整,从而得出最佳预测间隔。