Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty

TL;DR

Orthogonal Bootstrap is a novel method that efficiently reduces computational costs in bootstrap simulations of input uncertainty by decomposing the target into orthogonal and non-orthogonal parts, leveraging closed-form solutions.

Contribution

The paper introduces Orthogonal Bootstrap, a new approach that decomposes the bootstrap target to reduce Monte Carlo replications and computational expense.

Findings

Significantly reduces bootstrap computational cost.

Improves empirical accuracy of input uncertainty estimation.

Maintains the same confidence interval width.

Abstract

Bootstrap is a popular methodology for simulating input uncertainty. However, it can be computationally expensive when the number of samples is large. We propose a new approach called \textbf{Orthogonal Bootstrap} that reduces the number of required Monte Carlo replications. We decomposes the target being simulated into two parts: the \textit{non-orthogonal part} which has a closed-form result known as Infinitesimal Jackknife and the \textit{orthogonal part} which is easier to be simulated. We theoretically and numerically show that Orthogonal Bootstrap significantly reduces the computational cost of Bootstrap while improving empirical accuracy and maintaining the same width of the constructed interval.