发表机构
Indian Statistical Institute; University of California, Irvine（印度统计研究所; 加州大学欧文分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对空间依赖数据，提出一种基于顺序白化的共形预测方法，通过顺序条件化校准残差，实现精确有限样本覆盖率和渐近最优效率，在模拟和PM2.5应用中产生更窄更稳定的区间。
AI 中文摘要
分割共形预测利用保留（校准）数据上的预测误差来确定预测区间应有多宽。当这些误差与目标位置的误差可交换时，它保证了无分布假设的有限样本覆盖率。在空间依赖和非随机采样几何条件下，这一假设可能不成立。现有的空间方法使用拟合残差来从校准误差和目标误差中去除空间变化的可预测部分。然而，仅校准残差可预测的空间变化仍保留在目标误差和校准误差中，降低了区间的效率和稳定性。我们通过顺序地对校准残差进行条件化来解决这一问题，该方法通过最近邻近似可扩展到大型网络。在正确的工作协方差和椭圆残差分布假设下，所得区间在任何空间设计下都具有精确的有限样本覆盖率，并且在进一步条件下具有渐近最优效率。我们还限定了协方差误设下的覆盖率损失，并开发了一种诊断方法，用于识别存在覆盖不足风险的区域。在模拟数据中，我们的方法产生的区间比全局和局部的最先进替代方法更窄且更稳定。在全国PM2.5应用中，该方法在网络内产生更窄的区间，并识别出存在覆盖失败风险的区域。
英文摘要
Split conformal prediction uses prediction errors on held-out (calibration) data to determine how wide the prediction intervals should be. It guarantees distribution-free finite-sample coverage when these errors and the error at the target site are exchangeable. This assumption may fail under spatial dependence and nonrandom sampling geometry. Existing spatial methods use fitting residuals to remove the predictable part of spatial variation from calibration and target errors. However, the spatial variation that only the calibration residuals can predict remains in both the target and calibration errors, reducing the efficiency and stability of the interval. We address this by additionally conditioning on the calibration residuals sequentially, which scales to large networks through nearest-neighbour approximations. Under a correct working covariance and an elliptical residual law, the resulting interval has exact finite-sample coverage under any spatial design, and under further conditions it is asymptotically oracle efficient. We also bound coverage loss under covariance misspecification and develop a diagnostic that identifies regions at risk of undercoverage. In simulated data, our method produces narrower and more stable intervals than global and localized state-of-the-art alternatives. In a national PM2.5 application, it produces narrower intervals within the network and identifies regions at risk of coverage failure.
