发表机构
Faculty of Agriculture and Technology, University of South Bohemia; Natural Resources Institute Finland (Luke); University of Helsinki（南波希米亚大学农业与技术学院; 芬兰自然资源研究所（Luke）; 赫尔辛基大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种结合效应量与统计显著性的形式化图形推断框架，基于重采样和全局包络，实现强FWER控制，并应用于多元和函数线性模型。
AI 中文摘要
为了解决统计方法在评估实际效应量同时兼顾统计显著性的关键需求，我们引入了一个形式化图形推断框架，该框架将效应量与不确定性内在结合。基于重采样和全局包络，该方法具有通用性和直接的可视化解释性。现有包络检验仅能提供弱家族错误率（FWER）或错误发现率控制，我们通过引入新颖的逐步下降全局包络来推进该方法。我们从理论上证明，在可交换性条件下，其中几种包络能够实现精确的强FWER控制，从而保证对每个个体局部假设进行严格推断。除了提供调整后的$p$值外，该框架还为假设块提供调整后的子集$p$值，例如特定类别内协变量的函数效应。通过明确可视化效应的大小和方向相对于零假设下变异性的关系，我们的方法克服了传统检验的二分法性质，并提供了深刻的信息价值。所提出的框架应用于多元和函数线性模型。
英文摘要
To address the critical need for statistical methods that evaluate practical magnitude alongside statistical significance, we introduce a formal graphical inference framework that intrinsically combines effect size with uncertainty. Built upon resampling and global envelopes, this approach provides universality and direct visual interpretability. While existing envelope tests provide only weak family-wise error rate (FWER) or false discovery rate control, we advance the methodology by introducing novel step-down global envelopes. We theoretically prove that several of these envelopes achieve exact strong FWER control under exchangeability, guaranteeing rigorous inference for each individual local hypothesis. Beyond yielding adjusted $p$-values, the framework provides adjusted subset $p$-values for blocks of hypotheses, such as the functional effect of a covariate within a specific category. By explicitly visualizing the size and direction of the effect relative to its variability under the null hypothesis, our approach overcomes the dichotomous nature of traditional testing and provides profound informational value. The proposed framework is applied to multivariate and functional linear models.
