Conformal predictive systems are sets of predictive distributions with theoretical out-of-sample calibration guarantees. The calibration guarantees are typically that the set of predictions contains a forecast distribution whose prediction intervals exhibit the correct marginal coverage at all levels. Conformal predictive systems are constructed using conformity measures that quantify how well possible outcomes conform with historical data. However, alternative methods have been proposed to construct predictive systems with more appealing theoretical properties. We study an approach to construct predictive systems that we term Residual Distribution Predictive Systems. In the split conformal setting, this approach nests conformal predictive systems with a popular class of conformity measures, providing an alternative perspective on the classical approach. In the full conformal setting, the two approaches differ, and the new approach has the advantage that it does not rely on a conformity measure satisfying fairly stringent requirements to ensure that the predictive system is well-defined; it can readily be implemented alongside any point-valued regression method to yield predictive systems with out-of-sample calibration guarantees. The empirical performance of this approach is assessed using simulated data, where it is found to perform competitively with conformal predictive systems. However, the new approach offers considerable scope for implementation with alternative regression methods.

翻译：保形预测系统是一类具有理论外样本校准保证的预测分布集合。其校准保证通常表现为：预测集合中包含一个预测分布，该分布的预测区间在所有置信水平下均具有正确的边际覆盖率。保形预测系统通过一致性度量构建，该度量量化了可能结果与历史数据的符合程度。然而，已有研究提出替代方法以构建具有更优理论性质的预测系统。本文研究了一种称为残差分布预测系统的构建方法。在分割保形设定下，该方法嵌套了采用常用一致性度量类别的保形预测系统，为经典方法提供了新的视角。在全保形设定下，两种方法存在差异：新方法的优势在于不依赖满足严格条件的一致性度量即可确保预测系统定义良好；该方法可与任意点值回归方法结合，直接生成具有外样本校准保证的预测系统。通过模拟数据评估该方法的实证性能，发现其与保形预测系统具有相当竞争力。此外，新方法为结合其他回归方法实施提供了广阔空间。