Deterministic bootstrapping for a class of bootstrap methods

TL;DR

This paper introduces an efficient deterministic algorithm for approximating bootstrap distributions across various bootstrap methods, reducing computational effort and broadening applicability in hypothesis testing.

Contribution

The paper presents a novel deterministic algorithm that computes bootstrap distributions without repeated resampling, applicable to multiple bootstrap scenarios and hypothesis testing.

Findings

Reduces computational complexity of bootstrap distribution estimation

Applicable to mean, block, and residual bootstrap methods

Potentially broadens bootstrap applications in hypothesis testing

Abstract

An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp. input-derived data). In essence, the algorithm computes the distribution function from a linear mixture of independent random variables each having a finite discrete distribution. The algorithm is applicable to elementary bootstrap scenarios (targetting the mean as parameter of interest), for block bootstrap, as well as for certain residual bootstrap scenarios. Moreover, the algorithm promises a much broader applicability, in non-bootstrapped hypothesis testing.