A pooled percentile estimator for parallel simulations

Percentile is an important risk measure quantifying the stochastic system random behaviours. This paper studies a pooled percentile estimator, which is the sample percentile of detailed simulation outputs after directly pooling independent sample paths together. We derive the asymptotic representation of the pooled percentile estimator and further prove its normality. By comparing with the classical percentile estimator used in stochastic simulation, both theoretical and empirical studies demonstrate the advantages of the proposal under the context of parallel simulation.