We study the construction of a confidence interval (CI) for a simulation output performance measure that accounts for input uncertainty when the input models are estimated from finite data. In particular, we focus on performance measures that can be expressed as a ratio of two dependent simulation outputs' means. We adopt the parametric bootstrap method to mimic input data sampling and construct the percentile bootstrap CI after estimating the ratio at each bootstrap sample. The standard estimator, which takes the ratio of two sample averages, tends to exhibit large finite-sample bias and variance, leading to overcoverage of the percentile bootstrap CI. To address this, we propose two new ratio estimators that replace the sample averages with pooled mean estimators via the $k$-nearest neighbor ($k$NN) regression: the $k$NN estimator and the $k$LR estimator. The $k$NN estimator performs well in low dimensions but its theoretical performance guarantee degrades as the dimension increases. The $k$LR estimator combines the likelihood ratio (LR) method with the $k$NN regression, leveraging the strengths of both while mitigating their weaknesses; the LR method removes dependence on dimension, while the variance inflation introduced by the LR is controlled by $k$NN. Based on asymptotic analyses and finite-sample heuristics, we propose an experiment design that maximizes the efficiency of the proposed estimators and demonstrate their empirical performances using three examples including one in the enterprise risk management application.

翻译：本文研究当输入模型由有限数据估计时，构建考虑输入不确定性的仿真输出性能度量置信区间的方法。特别地，我们关注可表示为两个相关仿真输出均值之比的性能度量。我们采用参数自助法模拟输入数据抽样，并在每个自助样本中估计比率后构建百分位自助置信区间。标准估计器（即两个样本均值的比值）往往表现出较大的有限样本偏差和方差，导致百分位自助置信区间覆盖过度。为解决此问题，我们提出两种新的比率估计器：通过$k$近邻回归将样本均值替换为合并均值估计器的$k$NN估计器和$k$LR估计器。$k$NN估计器在低维情况下表现良好，但其理论性能保证随维度增加而下降。$k$LR估计器将似然比方法与$k$近邻回归相结合，在发挥两者优势的同时弥补其缺陷：似然比方法消除了对维度的依赖，而似然比引入的方差膨胀通过$k$近邻回归得到控制。基于渐近分析和有限样本启发式方法，我们提出了一种最大化所提估计器效率的实验设计方案，并通过包含企业风险管理应用在内的三个实例验证了其经验性能。