Confidence Intervals and Regions for Quantiles using Conditional Monte Carlo and Generalized Likelihood Ratios

Abstract

This article develops confidence intervals (CIs) and confidence regions (CRs) for quantiles based on independent realizations of a simulation response. The methodology uses a combination of conditional Monte Carlo (CMC) and the generalized likelihood ratio (GLR) method. While batching and sectioning methods partition the sample into nonoverlapping batches, and construct CIs and CRs by estimating the asymptotic variance using sample quantiles from each batch, the proposed techniques directly estimate the underlying probability density function of the response. Numerical results show that the CIs constructed by applying CMC, GLR, and sectioning lead to comparable coverage results, which are closer to the targets compared with batching alone for relatively small samples; and the coverage rates of the CRs constructed by applying CMC and GLR are closer to the targets than both sectioning and batching when the sample size is relatively small and the number of probability levels is relatively large.