Quantile Sensitivity Estimation

Quantiles are important performance characteristics that have been adopted in many areas for measuring the quality of service. Recently, sensitivity analysis of quantiles has attracted quite some attention. Sensitivity analysis of quantiles is particularly challenging as quantiles cannot be expressed as the expected value of some sample performance function, and it is therefore not evident how standard gradient estimation methods can be applied. In this paper we present a straightforward quantile sensitivity estimator based on measure-valued differentiation (MVD). We compare our new estimator with the known infinitesimal perturbation analysis (IPA) estimator and discuss implementation issues. Numerical examples will illustrate our results.