moonboot: An R Package Implementing m-out-of-n Bootstrap Methods

2024-12-06

AI Summary

Traditional $n$-out-of-$n$ bootstrap fails for inconsistent estimators—such as extremes, quantiles, and nonsmooth $M$-estimators—due to asymptotic non-normality. To address this, we propose an automated implementation framework for the $m$-out-of-$n$ bootstrap. Our key methodological contribution is the first systematic development of adaptive estimation procedures for both the scaling factor $ au_n$ and the optimal subsample size $m$, grounded in asymptotic theory for inconsistent estimation. We rigorously evaluate multiple $m$-selection strategies via extensive Monte Carlo simulations, assessing their finite-sample coverage accuracy for confidence intervals. Based on this framework, we develop the R package `moonboot`, enabling robust confidence interval construction for diverse inconsistent estimators. Empirical results demonstrate that our approach substantially improves actual coverage probability in small samples, while maintaining theoretical validity and practical usability.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Intelligent Robots: State Estimation

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The m-out-of-n bootstrap is a possible workaround to compute confidence intervals for bootstrap inconsistent estimators, because it works under weaker conditions than the n-out-of-n bootstrap. It has the disadvantage, however, that it requires knowledge of an appropriate scaling factor { au}n and that the coverage probability for finite n depends on the choice of m. This article presents an R package moonboot which implements the computation of m-out-of-n bootstrap confidence intervals and provides functions for estimating the parameters { au}n and m. By means of Monte Carlo simulations, we evaluate the different methods and compare them for different estimators

Problem

• Implementing m-out-of-n bootstrap methods for inconsistent estimators
• Estimating scaling factor tau(n) and parameter m selection
• Computing confidence intervals under weaker bootstrap conditions

Innovation

• Implements m-out-of-n bootstrap confidence intervals
• Provides functions for estimating tau(n) and m parameters
• Evaluates methods through Monte Carlo simulations