Adaptive Bag of Little Bootstraps for Nonsmooth Robust Inference: A Stability-Driven Framework with Reproducible Cholera Surveillance Illustration from the Democratic Republic of the Congo

Abstract

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 {\gamma} in m=n^{\gamma}is 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.