Variance reduction of quantile estimates via nonlinear control
WSC '89 Proceedings of the 21st conference on Winter simulation
Control variates for quantile estimation
Management Science
Operations Research
Variance reduction for quantile estimation via correlation induction
WSC '92 Proceedings of the 24th conference on Winter simulation
S an Interactive Environment for Data Analysis and Graphics
S an Interactive Environment for Data Analysis and Graphics
Options pricing: using simulation for option pricing
Proceedings of the 32nd conference on Winter simulation
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To estimate selected quantiles of the response of a finite-horizon simulation, we develop statistical methods based on correlation-induction techniques for variance reduction, with emphasis on antithetic variates and Latin hypercube sampling. The proposed multiple-sample quantile estimator is the average of negatively correlated quantile estimators computed from disjoint samples of the response, where negative correlation is induced between corresponding responses in different samples while mutual independence of responses is maintained within each sample. The proposed single-sample quantile estimator is computed from negatively correlated responses within one overall sample. We establish a central limit theorem for the single-sample estimator based on Latin hypercube sampling, showing that asymptotically this estimator is unbiased and has smaller variance than the comparable direct-simulation estimator based on independent replications. We also show that if the response is monotone in the simulation's random-number inputs and if the response satisfies some other regularity conditions, then asymptotically the multiple-sample estimator is unbiased and has smaller mean square error than the direct-simulation estimator.