Technical note—Constructing confidence intervals for nested simulation
针对嵌套模拟中不同形式的泛函，建立了具有渐近最优收敛速度的中心极限定理，并基于此开发了一个统一的置信区间框架，确保点估计的均方误差和置信区间宽度都达到最优收敛速度。
Abstract Nested simulation is typically used to estimate the functional of a conditional expectation. Considerable research has been performed on point estimation for various functionals. However, the quantification of the statistical uncertainty in the point estimator, for instance, using confidence intervals (CIs), has not been extensively investigated. In this article, we establish central limit theorems with the asymptotically optimal convergence rate of for nested simulation with different forms of functionals, where denotes the total computational effort. Based on these theorems, we develop a unified CI framework that can ensure that both the mean squared error of the point estimator and CI width attain the optimal convergence rate. Numerical examples are presented, and the results are found to be consistent with the theoretical results. Experimental results demonstrate that the proposed framework outperforms the existing methods for CI construction in terms of the CI widths and convergence rates.