发表机构
University of Science and Technology of China; City University of Hong Kong; Nanyang Technological University（中国科学技术大学; 香港城市大学; 南洋理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对E值通用阈值偏保守的问题，采用非递减与L-Lipschitz密度模型改进阈值，将其应用于多重检验与序贯检验，通过数值实验验证了方法的增益。
AI 中文摘要
E值为统计推断提供了灵活框架，但当原分布存在额外结构时，通用阈值1/α可能偏保守。我们研究结构限制如何限制马尔可夫不等式背后的最坏情况集中度，采用非递减密度模型约束尾部分配，用L-Lipschitz密度模型控制局部集中度。非递减模型给出极小极大拒绝阈值，Lipschitz条件产生更精确的闭式阈值，相对1/α有O(L^{-1/2})的改进。我们进一步证明，当α→0时该阈值渐近精确，即无一致有效的阈值能以固定正的L相关量对其改进。随后将Lipschitz校准纳入控制FDR的多重检验程序，利用相同结构信息为随时有效序贯推断构建校准条件E值。数值实验表明，所得方法在发现结果上有增益，且序贯程序存在权衡。
英文摘要
E-values provide a flexible framework for statistical inference, but the universal threshold $1/α$ can be conservative when the null distribution has additional structure. We study how structural restrictions limit the worst-case concentration underlying Markov's inequality, using a nondecreasing density model to constrain tail allocation and an $L$-Lipschitz density model to control local concentration. The nondecreasing model gives the minimax rejection threshold, and the Lipschitz condition yields a sharper closed-form threshold with an $O(L^{-1/2})$ relative improvement over $1/α$. We further show that this threshold is asymptotically sharp as $α\to0$, in the sense that no uniformly valid threshold can improve on it by a fixed positive $L$-dependent amount. We then incorporate the Lipschitz calibration into multiple testing procedures with FDR control and use the same structural information to construct calibrated conditional e-values for anytime-valid sequential inference. Numerical experiments illustrate the resulting gains in discoveries and the trade-offs of the sequential procedures.
