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Correlation-induction techniques for estimating quantiles in simulation experiments

Correlation-induction techniques for estimating quantiles in simulation experiments
Correlation-induction techniques for estimating quantiles in simulation experiments
A simulation-based quantile estimator measures the level of system performance that can be delivered with a prespecified probability. To estimate selected quantiles of the response of a finite-horizon simulation, we develop procedures based on correlation induction techniques for variance reduction, with emphasis on antithetic variates and Latin hypercube sampling. These procedures achieve improved precision by controlling the simulation's random-number inputs as an integral part of the experimental design. The proposed multiple-sample quantile estimator is the average of negatively correlated quantile estimators computed from disjoint samples of the simulation 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 simulation responses within one all-inclusive sample. The single-sample estimator based on Latin hypercube sampling is shown to be asymptotically normal and unbiased with smaller variance than the comparable direct-simulation estimator based on independent replications. Similar asymptotic comparisons of the multiple-sample and direct-simulation estimators focus on bias and mean square error. Monte Carlo results suggest that the proposed procedures can yield significant reductions in bias, variance, and mean square error when estimating quantiles of the completion time of a stochastic activity network.
simulation efficiency, variance reduction techniques, design of experiments, antithetic variates, latin hypercube sampling, Simulation, statistical analysis, single- multiple-sample quantile estimators
0030-364X
574-591
Avramidis, Athanassios N.
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Wilson, James R.
938b5976-c9c4-42a5-8ec9-4b36266347bb
Avramidis, Athanassios N.
d6c4b6b6-c0cf-4ed1-bbe1-a539937e4001
Wilson, James R.
938b5976-c9c4-42a5-8ec9-4b36266347bb

Avramidis, Athanassios N. and Wilson, James R. (1998) Correlation-induction techniques for estimating quantiles in simulation experiments. Operations Research, 46 (4), 574-591. (doi:10.1287/opre.46.4.574).

Record type: Article

Abstract

A simulation-based quantile estimator measures the level of system performance that can be delivered with a prespecified probability. To estimate selected quantiles of the response of a finite-horizon simulation, we develop procedures based on correlation induction techniques for variance reduction, with emphasis on antithetic variates and Latin hypercube sampling. These procedures achieve improved precision by controlling the simulation's random-number inputs as an integral part of the experimental design. The proposed multiple-sample quantile estimator is the average of negatively correlated quantile estimators computed from disjoint samples of the simulation 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 simulation responses within one all-inclusive sample. The single-sample estimator based on Latin hypercube sampling is shown to be asymptotically normal and unbiased with smaller variance than the comparable direct-simulation estimator based on independent replications. Similar asymptotic comparisons of the multiple-sample and direct-simulation estimators focus on bias and mean square error. Monte Carlo results suggest that the proposed procedures can yield significant reductions in bias, variance, and mean square error when estimating quantiles of the completion time of a stochastic activity network.

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More information

Published date: July 1998
Keywords: simulation efficiency, variance reduction techniques, design of experiments, antithetic variates, latin hypercube sampling, Simulation, statistical analysis, single- multiple-sample quantile estimators
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 336781
URI: http://eprints.soton.ac.uk/id/eprint/336781
ISSN: 0030-364X
PURE UUID: d8035124-313d-47e8-b473-b061087665fd
ORCID for Athanassios N. Avramidis: ORCID iD orcid.org/0000-0001-9310-8894

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Date deposited: 13 Apr 2012 09:02
Last modified: 15 Mar 2024 03:29

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Author: James R. Wilson

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