Saddlepoint approximations for plug-in resampling
插件式重抽样的鞍点近似AI 解读 ↓
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插件式重抽样的鞍点近似
- 研究问题
- 研究问题：在稀疏、大规模检验问题中，重抽样方法虽优于正态近似但计算代价过高；摘要关注能否用解析的鞍点尾部近似替代插件式重抽样，并在可验证的条件下给出近似误差保证。
- 方法与思路
- 方法思路：作者将若干现有程序归为更快的插件式重抽样子类，在重抽样时固定已拟合的冗余参数；当重抽样统计量为条件独立项之和时，用 Lugannani–Rice 鞍点近似替代重抽样，并采用不同于 Edgeworth 界的方法建立有限样本相对误差界。
- 材料陈述的贡献
- 摘要所述贡献：给出更易验证条件下 Lugannani–Rice 近似的有限样本相对误差界；在统计遗传学中把响应重抽样程序识别为已有鞍点近似的目标并给出代表性设定下的保证；为 distilled conditional randomization test 提出鞍点近似，速率刻画稀疏性与信号强度影响，特殊情形有匹配下界，并建立渐近第一类错误控制。
- 阅读关注点
- 阅读时应核对：插件式重抽样子类的界定条件、条件独立项之和假设是否适用、有限样本相对误差界所需的具体正则条件、速率与下界对应的特殊情形，以及模拟与单细胞 CRISPR 数据分析中加速倍数与统计性能的比较设置。
- 阅读边界
- 摘要信息的边界：仅凭摘要无法判断定理证明细节、正则条件的实际可检验性、下界的一般性，以及 250 倍加速所依赖的具体数据规模；摘要未说明模拟设计、样本量与代码可得性。该文为 online-first 版本，不能据此声称已见刊定稿。
原文摘要
Abstract Resampling-based procedures can improve on normal approximations in sparse, large-scale testing problems, but their computational cost can be prohibitive. We recognize that several existing procedures belong to a faster plug-in resampling subclass, fixing fitted nuisance parameters during resampling. When the resampled statistic is a sum of conditionally independent terms, the saddlepoint approximation for the resampling p -value offers further acceleration, replacing resampling with an analytical tail approximation. However, standard Edgeworth-based approximation-error bounds impose regularity conditions that are hard to verify for plug-in resampling laws. We use an alternative approach to establish a finite-sample relative-error bound for the Lugannani–Rice approximation under more tractable conditions, which we apply in two contexts. In statistical genetics, we identify response resampling procedures as the targets of existing saddlepoint approximations and establish guarantees in a representative setting. In conditional independence testing, we introduce a saddlepoint approximation for the distilled conditional randomization test, which has been applied successfully in biology. Our rates quantify the effects of sparsity and signal strength, with matching lower bounds in special cases. We additionally establish asymptotic Type-I error control of the corresponding plug-in resampling procedures under growing sparsity. In simulations and single-cell CRISPR data analysis, our new test closely approximates distilled conditional randomization test p -values and preserves its statistical performance while accelerating computation by up to 250-fold.