AI 中文总结
本文针对任意依赖下相关p值函数的置信域计算问题，提出无需网格的精确方法，开发含自适应多分位数轮廓聚合器的精确投票算法，实验显示其推断稳定鲁棒且运行时间大幅提升。
AI 中文摘要
重复样本拆分、交叉拟合、保形集成及相关随机化工作流常为同一目标生成多个相关的有效p值函数。现有p值合并理论在任意依赖下保证逐点有效性，但要将合并输出转化为置信域，通常需要对参数空间上的网格进行重复评估，该逆步骤计算成本高、依赖近似，且难以扩展。本文研究何时可从拆分区域精确计算置信域，无需对参数空间网格化。主要结构结果表明，由步校准器诱导的合并器在区域层面构成广泛的可精确执行类别；校准器诱导类别内的部分逆结果显示，可精确执行性与步结构密切相关。在该类别内，本文开发了精确投票算法，包括自适应多分位数轮廓聚合器，其无需预先指定单个顺序统计量阈值，同时在任意依赖下保持有限样本有效性。对重复拆分回归和保形预测的模拟研究，以及真实数据回归示例表明，所提方法提供了稳定、面向鲁棒性的精确推断，与网格逆比较器相比运行时间大幅提升。网格分辨率基准显示，固定k投票和自适应多分位数投票对逆网格细化基本不敏感；多维单阈值压力测试则说明，在简单盒几何设置中，网格逆基线面临维度爆炸问题。综上，结果表明，任意依赖下的轮廓合并可转化为可精确执行的区域计算框架，而非仅为逐点有效性工具。
英文摘要
Repeated sample splitting, cross-fitting, conformal ensembling, and related randomized workflows often produce multiple dependent valid p-value functions for the same target. Existing p-merging theory guarantees pointwise validity under arbitrary dependence, but turning the merged output into a confidence region typically requires repeated evaluation on a grid over the parameter space. This inversion step can be computationally costly, approximation-dependent, and increasingly difficult to scale. We study when confidence regions can instead be computed exactly from split-wise regions without gridding the parameter space. Our main structural result shows that mergers induced by step calibrators form a broad exactly executable class at the region level, and a partial converse within the calibrator-induced family indicates that exact executability is closely tied to step structure. Within this class, we develop exact voting algorithms, including an adaptive multi-quantile contour aggregator that avoids pre-specifying a single order-statistic threshold while preserving finite-sample validity under arbitrary dependence. Simulation studies on repeated-split regression and conformal prediction, together with real-data regression examples, show that the proposed methods provide stable, robustness-oriented exact inference with substantial runtime gains over grid-inversion comparators. A grid-resolution benchmark shows that fixed-k voting and adaptive multi-quantile voting are essentially insensitive to inversion-grid refinement, while a multidimensional single-threshold stress test illustrates the dimensional blow-up faced by grid-inversion baselines in a simple box-geometry setting. Taken together, the results show that arbitrary-dependence contour merging can be turned into an exactly executable region-computation framework rather than merely a pointwise validity device.
DOI：10.1080/00949655.2026.2723318
