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.

翻译：Bootstrap是模拟输入不确定性的常用方法，但当样本量较大时，其计算成本可能很高。我们提出一种名为\textbf{正交Bootstrap}的新方法，可减少所需的蒙特卡洛复制次数。我们将待模拟目标分解为两部分：具有闭式解（称为无穷小刀切法）的\textit{非正交部分}与更易模拟的\textit{正交部分}。我们通过理论和数值实验证明，正交Bootstrap显著降低了Bootstrap的计算成本，同时提高了经验精度，并保持了所构建区间的相同宽度。