On the asymptotic analysis of quantile sensitivity estimation by Monte Carlo simulation

We provide a unified framework to treat the asymptotic analysis for the non-batched quantile sensitivity estimators of Fu et al. (2009), Liu and Hong (2009), and Lei et al. (2017). With only mild differences in regularity conditions and proofs, asymptotic results including strong consistency and a central limit theorem are established for all three estimators. Simulation results substantiate the theoretical analysis.