Adaptive sequential procedures for quantile selection with importance sampling

In this article, we consider the problem of identifying the simulated system configuration with optimal quantile performance among a finite set of alternative systems. We first propose adaptive sequential selection procedures via direct simulation, where the point and variance estimators for quantiles are sequentially updated. For the sake of extreme quantiles, we develop adaptive quantile selection procedures using importance sampling. Our procedures apply the sample average approximation and the stochastic approximation for iteratively computing the optimal importance-sampling parameter and the importance-sampling quantile estimators. The statistical validity of the proposed selection procedures is proven in the asymptotic regime. We particularly investigate the consistency and the central limit convergence using both sample average and stochastic approximation for quantile estimation during the adaptive procedures. Empirical results and an illustrative example show the efficiency of the developed procedures.