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Variance estimation and sequential stopping in steady-state simulations using linear regression

Variance estimation and sequential stopping in steady-state simulations using linear regression We propose a method for estimating the variance parameter of a discrete, stationary stochastic process that involves combining variance estimators at different run lengths using linear regression. We show that the estimator thus obtained is first-order unbiased and consistent under two distinct asymptotic regimes. In the first regime, the number of constituent estimators used in the regression is fixed and the numbers of observations corresponding to the component estimators grow in a proportional manner. In the second regime, the number of constituent estimators grows while the numbers of observations corresponding to each estimator remain fixed. We also show that for m-dependent stochastic processes, one can use regression to obtain asymptotically normally distributed variance estimators in the second regime. Analytical and numerical examples indicate that the new regression-based estimators give good mean-squared-error performance in steady-state simulations. The regression methodology presented in this article can also be applied to estimate the bias of variance estimators. As an example application, we present a new sequential-stopping rule that uses the estimate for bias to determine appropriate run lengths. Monte Carlo experiments indicate that this bias-controlling sequential-stopping method has the potential to work well in practice. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Modeling and Computer Simulation (TOMACS) Association for Computing Machinery

Variance estimation and sequential stopping in steady-state simulations using linear regression

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 ACM
ISSN
1049-3301
eISSN
1558-1195
DOI
10.1145/2567907
Publisher site
See Article on Publisher Site

Abstract

We propose a method for estimating the variance parameter of a discrete, stationary stochastic process that involves combining variance estimators at different run lengths using linear regression. We show that the estimator thus obtained is first-order unbiased and consistent under two distinct asymptotic regimes. In the first regime, the number of constituent estimators used in the regression is fixed and the numbers of observations corresponding to the component estimators grow in a proportional manner. In the second regime, the number of constituent estimators grows while the numbers of observations corresponding to each estimator remain fixed. We also show that for m-dependent stochastic processes, one can use regression to obtain asymptotically normally distributed variance estimators in the second regime. Analytical and numerical examples indicate that the new regression-based estimators give good mean-squared-error performance in steady-state simulations. The regression methodology presented in this article can also be applied to estimate the bias of variance estimators. As an example application, we present a new sequential-stopping rule that uses the estimate for bias to determine appropriate run lengths. Monte Carlo experiments indicate that this bias-controlling sequential-stopping method has the potential to work well in practice.

Journal

ACM Transactions on Modeling and Computer Simulation (TOMACS) – Association for Computing Machinery

Published: Feb 1, 2014

Keywords: Stationary processes

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