AI 中文总结
本研究提出自适应小袋自助法（BLB），通过数据驱动准则选择指数γ，实现非光滑估计量的鲁棒推断，Python包robustboot实现该方法，经模拟和霍乱监测示例验证，其区间覆盖率更高且计算效率良好。
AI 中文摘要
自助法推断是计算统计学的基石，但经典自助法和BCa区间对于经验分位数、样本最大值、特征值比率及最大相关性等非光滑估计量可能不稳定。m选n自助法可减少部分失效模式，但速度较慢且对所选子抽样高度敏感。本研究提出自适应小袋自助法（BLB），其中m=n^γ中的指数γ由数据驱动准则选择，该准则结合了插件渐近均方误差（AMSE）原理与BLB方差估计器的稳定性风险代理。Python包robustboot实现了所提方法，同时包含BCa对照方法、非光滑统计量、检验及分位数推断、特征值比率推断、最大相关性筛选的可重复示例。研究提供了明确算法、理论假设、有限候选网格上的一致性结果、跨多样本量的广泛蒙特卡洛验证，以及所选指数的敏感性诊断。模拟研究表明，自适应BLB相较于普通自助法提高了区间覆盖率，同时保持了计算效率。来自刚果民主共和国的精选汇总霍乱监测示例，展示了公共卫生阈值的鲁棒不确定性量化，且未夸大重构数据。
英文摘要
Bootstrap inference is a cornerstone of computational statistics, but classical bootstrap and BCa intervals can be unstable for nonsmooth estimators such as empirical quantiles, sample maxima, eigenvalue ratios and maximum correlations. The m-out-of-n bootstrap can reduce some failure modes, but it is slow and highly sensitive to the chosen subsampling size. This work develops an adaptive Bag of Little Bootstraps (BLB) procedure in which the exponent γ in m=n^γis selected by a data-driven criterion combining a plug-in asymptotic mean squared error (AMSE) principle with a stability-risk proxy for the BLB variance estimator. The Python package robustboot implements the proposed method together with BCa comparators, nonsmooth statistics, tests, and reproducible examples for quantile inference, eigenvalue-ratio inference, and maximum-correlation screening. We provide an explicit algorithm, theoretical assumptions, a consistency result on a finite candidate grid, extensive Monte Carlo validation across multiple sample sizes, and sensitivity diagnostics for the selected exponent. Simulation studies show that the adaptive BLB improves interval coverage relative to the ordinary bootstrap while preserving computational efficiency. A curated aggregate cholera surveillance illustration from the Democratic Republic of the Congo demonstrates robust uncertainty quantification for public-health thresholds without overstating reconstructed data.
