Orthogonal Bootstrap: Efficient Simulation of Input Uncertainty

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 $\mathbf{\text{Orthogonal}}\mathbf{\text{Bootstrap}}$ that reduces the number of required Monte Carlo replications. We decomposes the target being simulated into two parts: the $\mathit{\text{non-orthogonal}}\mathit{\text{part}}$ which has a closed-form result known as Infinitesimal Jackknife and the $\mathit{\text{orthogonal}}\mathit{\text{part}}$ 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.