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Computing Densities for Markov Chains via Simulation

Author

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  • Shane G. Henderson

    () (Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI 48109-2117)

  • Peter W. Glynn

    () (Management Science and Engineering, Terman Engineering Center, Stanford University, Stanford, CA 94305-4026)

Abstract

We introduce a new class of density estimators, termed look-ahead density estimators, for performance measures associated with a Markov chain. Look-ahead density estimators are given for both transient and steady-state quantities. Look-ahead density estimators converge faster (especially in multidimensional problems) and empirically give visually superior results relative to more standard estimators, such as kernel density estimators. Several numerical examples that demonstrate the potential applicability of look-ahead density estimation are given.

Suggested Citation

  • Shane G. Henderson & Peter W. Glynn, 2001. "Computing Densities for Markov Chains via Simulation," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 375-400, May.
  • Handle: RePEc:inm:ormoor:v:26:y:2001:i:2:p:375-400
    DOI: 10.1287/moor.26.2.375.10562
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    File URL: http://dx.doi.org/10.1287/moor.26.2.375.10562
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    References listed on IDEAS

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    1. Athanassios N. Avramidis & James R. Wilson, 1996. "Integrated Variance Reduction Strategies for Simulation," Operations Research, INFORMS, vol. 44(2), pages 327-346, April.
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    3. Yakowitz, Sidney, 1989. "Nonparametric density and regression estimation for Markov sequences without mixing assumptions," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 124-136, July.
    4. P. Heidelberger & P. A. W. Lewis, 1984. "Quantile Estimation in Dependent Sequences," Operations Research, INFORMS, vol. 32(1), pages 185-209, February.
    5. Athanassios N. Avramidis & James R. Wilson, 1998. "Correlation-Induction Techniques for Estimating Quantiles in Simulation Experiments," Operations Research, INFORMS, vol. 46(4), pages 574-591, August.
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    Cited by:

    1. Azariadis, Costas & Stachurski, John, 2005. "Poverty Traps," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.),Handbook of Economic Growth, edition 1, volume 1, chapter 5, Elsevier.
    2. John Stachurski & Vance Martin, 2008. "Computing the Distributions of Economic Models via Simulation," Econometrica, Econometric Society, vol. 76(2), pages 443-450, March.
    3. R. Anton Braun & Huiyu Li & John Stachurski, 2012. "Generalized Look-Ahead Methods for Computing Stationary Densities," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 489-500, August.
    4. Christian Gourieroux & Joann Jasiak, 2016. "Filtering, Prediction and Simulation Methods for Noncausal Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 405-430, May.
    5. R. Anton Braun & Huiyu Li & John Stachurski, 2011. "Generalized Look-Ahead Methods for Computing Stationary Densities," ANU Working Papers in Economics and Econometrics 2011-558, Australian National University, College of Business and Economics, School of Economics.
    6. Richard Anton Braun & Huiyu Li & John Stachurski, 2009. "Computing Densities: A Conditional Monte Carlo Estimator," CIRJE F-Series CIRJE-F-678, CIRJE, Faculty of Economics, University of Tokyo.
    7. Richard Anton Braun & Huiyu Li & John Stachurski, 2009. "Computing Densities and Expectations in Stochastic Recursive Economies: Generalized Look-Ahead Techniques," CIRJE F-Series CIRJE-F-620, CIRJE, Faculty of Economics, University of Tokyo.
    8. John Stachurski & Huiyu Li & Richard Anton Braun, 2009. "Computing Densities in Stochastic Recursive Economies: Generalized Look-Ahead Techniques," 2009 Meeting Papers 975, Society for Economic Dynamics.

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