Department of Economics, Massachusetts Institute of Technology, Cambridge, MA 02142.
Center for Statistics and Data Science, Massachusetts Institute of Technology, Cambridge, MA 02142.
Proc Natl Acad Sci U S A. 2021 Nov 30;118(48). doi: 10.1073/pnas.2107794118.
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, -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, under overfitting, and with time series data. We also propose a simple "shape" adjustment of our baseline method that yields optimal prediction intervals.
我们提出了一种基于条件分布模型（如分位数回归和分布回归）构建条件有效预测区间的稳健方法。我们的方法可应用于重要的预测问题，包括横截面预测、-步预测、合成控制和反事实预测以及个体治疗效果预测。我们的方法利用概率积分变换，并依赖于排列估计秩。与回归残差不同，秩与预测变量无关，这使我们能够在异方差条件下构建条件有效预测区间。我们在一致估计下建立了近似条件有效性，并在模型误设定、过拟合和时间序列数据下提供了近似无条件有效性。我们还提出了对我们的基准方法进行简单的“形状”调整，从而得到最优预测区间。
