Generative modeling for the bootstrap

2026-02-18

AI Summary

This work proposes a modern smoothed bootstrap method grounded in generative modeling to address the limitations of traditional bootstrap approaches—such as Efron’s bootstrap—in high-dimensional, non-regular, or root-n inconsistent settings where valid statistical inference is otherwise challenging. By synthesizing new samples from the observed data, the proposed framework enables reliable inference for both regular and irregular estimators. The method retains theoretical validity even under nonstandard asymptotic regimes and high-dimensional configurations, yielding statistically sound confidence intervals. Consequently, it substantially extends the applicability and robustness of bootstrap-based inference beyond conventional scenarios.

Technology Category

Reasoning under Uncertainty: Probabilistic InferenceMachine Learning: Calibration & Uncertainty QuantificationIntelligent Robots: State Estimation

Application Category

Web Mining and Content Analysis: Robustness and generalizability of Web mining methodsUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalizationEconomics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• bootstrap
• generative modeling
• confidence intervals
• irregular estimators
• curse of dimensionality

Innovation

• generative modeling
• bootstrap inference
• smoothed bootstrap
• irregular estimators
• curse of dimensionality