Adaptive Generative Bootstrap: A Robust Inference Method for Small and Multimodal Samples

Abstract

The standard nonparametric bootstrap performs reliably across many settings, but small samples n<30 and multimodal data tend expose its limitations under-coverage and discreetness artifacts are the most commonly reported problems. We developed an Adaptive Generative Bootstrap (AGB) method to directly address these gaps. Rather than resampling from the observed data, generative sampling is drawn from a variable-bandwidth kernel density estimate (KDE), with bandwidths adapted locally through Abramson's square root scaling. That adaptation carries a concrete theoretical payoff: under the regularity conditions set out in Section 2 and Appendix A, the leading pointwise bias of the adaptive KDE is reduced from \(O\left(h^2\right)\) to \(O\left(h^4\right)\). It should be noted, however, that this result pertains to the density estimator itself, not to bootstrap coverage properties directly. For that reason, the finite-sample inferential behavior of AGB is assessed empirically through Monte Carlo simulations and benchmark examples, with coverage probability, interval length, bias, and RMSE serving as the primary performance criteria.