Estimating Confidence Intervals and Regions for Quantiles in Steady‐State Simulations
针对稳态模拟中的分位数，提出了基于批处理、分段和广义似然比的方法来构建置信区间和置信区域，并通过数值实验验证了有效性。
ABSTRACT We propose methods based on batching, sectioning, and generalized likelihood ratios (GLRs) for computing confidence intervals (CIs) and confidence regions (CRs) for quantiles in steady‐state simulations. Based on central limit theorems for quantile estimators, CIs and CRs can be computed from a single batch of simulated output using a GLR method to consistently estimate the unknown density function. This paper makes the following contributions: (1) We derive a GLR estimator for distribution sensitivities in the steady‐state setting and, under the geometric‐moment contraction (GMC) conditions, we establish the uniform consistency of the GLR estimators and the asymptotic validity of the respective CIs and CRs for quantiles. (2) We also establish the asymptotic validity of CIs and CRs for quantiles by batching and sectioning methods for steady‐state simulations. Numerical experiments demonstrate the validity of the aforementioned methods as the coverage rates of the CIs and CRs approach the target levels for appropriately large sample sizes. In the steady‐state setting, the sectioning and GLR methods demonstrate their respective advantages in different examples.