Submitted to Operations Research manuscript OPRE-2014-08-465-final Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named jour- nal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication. Quantile Estimation With Latin Hypercube Sampling Hui Dong Supply Chain Management and Marketing Sciences Dept., Rutgers Univ., Newark, NJ 07102, huidong@rutgers.edu Marvin K. Nakayama Computer Science Department, New Jersey Institute of Technology, Newark, NJ 07102, marvin@njit.edu Quantiles are often used to measure risk of stochastic systems. We examine quantile estimators obtained using simulation with Latin hypercube sampling (LHS), a variance-reduction technique that efficiently extends stratified sampling to higher dimensions and produces negatively correlated outputs. We consider single- sample LHS (ssLHS), which minimizes the variance that can be obtained from LHS, and also replicated LHS (rLHS). We develop a consistent estimator of the asymptotic variance of the ssLHS quantile estimator’s central limit theorem, enabling us to provide the first confidence interval (CI) for a quantile when applying ssLHS. For rLHS, we construct CIs using batching and sectioning. On average, our rLHS CIs are shorter than previous rLHS CIs and only slightly wider than the ssLHS CI. We establish the asymptotic validity of the CIs by first proving that the quantile estimators satisfy Bahadur representations, which show that the quantile estimators can be approximated by linear transformations of estimators of the cumulative distribution function (CDF). We present numerical results comparing the various CIs. Key words : simulation: efficiency, statistical analysis; reliability: system safety History : 1. Introduction For a given constant 0 <p< 1, the p-quantile of a continuous random variable Y is a constant such that Y has probability p of lying below the constant. We can also express the p-quantile in terms of the inverse of the CDF of Y . For example, the median corresponds to the 0.5-quantile. 1