Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty
This addresses efficiency for practitioners using bootstrap methods in statistical simulation, though it appears incremental as an optimization of existing methodology.
The paper tackles the computational expense of bootstrap methods for simulating input uncertainty by proposing Orthogonal Bootstrap, which decomposes the target into non-orthogonal and orthogonal parts to reduce Monte Carlo replications. The result shows significant computational cost reduction while improving empirical accuracy and maintaining interval width.
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.