Generative modeling for the bootstrap

TL;DR

This paper introduces a generative modeling approach for bootstrap inference that provides valid confidence intervals even in complex, high-dimensional, or irregular estimation scenarios, surpassing traditional bootstrap limitations.

Contribution

It demonstrates that generative modeling can serve as a robust foundation for bootstrap methods, extending their applicability to challenging estimation settings.

Findings

Provides statistically valid confidence intervals for irregular estimators.

Remains effective in high-dimensional and non-Gaussian regimes.

Surpasses traditional bootstrap in scenarios where Efron's bootstrap fails.

Abstract

Generative modeling builds on and substantially advances the classical idea of simulating synthetic data from observed samples. This paper shows that this principle is not only natural but also theoretically well-founded for bootstrap inference: it yields statistically valid confidence intervals that apply simultaneously to both regular and irregular estimators, including settings in which Efron's bootstrap fails. In this sense, the generative modeling-based bootstrap can be viewed as a modern version of the smoothed bootstrap: it could mitigate the curse of dimensionality and remain effective in challenging regimes where estimators may lack root-$n$ consistency or a Gaussian limit.