IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v116y2006i5p724-756.html
   My bibliography  Save this article

Worst-case large-deviation asymptotics with application to queueing and information theory

Author

Listed:
  • Pandit, Charuhas
  • Meyn, Sean

Abstract

An i.i.d. process is considered on a compact metric space . Its marginal distribution [pi] is unknown, but is assumed to lie in a moment class of the form, where {fi} are real-valued, continuous functions on , and {ci} are constants. The following conclusions are obtained: (i) For any probability distribution [mu] on , Sanov's rate-function for the empirical distributions of is equal to the Kullback-Leibler divergence D([mu][short parallel][pi]). The worst-case rate-function is identified as where f=(1,f1,...,fn)T, and is a compact, convex set. (ii) A stochastic approximation algorithm for computing L is introduced based on samples of the process . (iii) A solution to the worst-case one-dimensional large-deviation problem is obtained through properties of extremal distributions, generalizing Markov's canonical distributions. (iv) Applications to robust hypothesis testing and to the theory of buffer overflows in queues are also developed.

Suggested Citation

  • Pandit, Charuhas & Meyn, Sean, 2006. "Worst-case large-deviation asymptotics with application to queueing and information theory," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 724-756, May.
  • Handle: RePEc:eee:spapps:v:116:y:2006:i:5:p:724-756
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00164-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. James E. Smith, 1995. "Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis," Operations Research, INFORMS, vol. 43(5), pages 807-825, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    2. Laurent El Ghaoui & Maksim Oks & Francois Oustry, 2003. "Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach," Operations Research, INFORMS, vol. 51(4), pages 543-556, August.
    3. Henry Lam & Clementine Mottet, 2017. "Tail Analysis Without Parametric Models: A Worst-Case Perspective," Operations Research, INFORMS, vol. 65(6), pages 1696-1711, December.
    4. Nikolaus Schweizer & Nora Szech, 2018. "Optimal Revelation of Life-Changing Information," Management Science, INFORMS, vol. 64(11), pages 5250-5262, November.
    5. Ran, Cuiling & Zhang, Yanzi & Yin, Ying, 2021. "Demand response to improve the shared electric vehicle planning: Managerial insights, sustainable benefits," Applied Energy, Elsevier, vol. 292(C).
    6. Li, Xiaobo & Natarajan, Karthik & Teo, Chung-Piaw & Zheng, Zhichao, 2014. "Distributionally robust mixed integer linear programs: Persistency models with applications," European Journal of Operational Research, Elsevier, vol. 233(3), pages 459-473.
    7. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.
    8. Zuluaga, Luis F. & Peña, Javier & Du, Donglei, 2009. "Third-order extensions of Lo's semiparametric bound for European call options," European Journal of Operational Research, Elsevier, vol. 198(2), pages 557-570, October.
    9. Derek Singh & Shuzhong Zhang, 2020. "Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures," Papers 2010.05398, arXiv.org, revised Oct 2020.
    10. Villegas, Andrés M. & Medaglia, Andrés L. & Zuluaga, Luis F., 2012. "Computing bounds on the expected payoff of Alternative Risk Transfer products," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 271-281.
    11. Zhaolin Li & Samuel N. Kirshner, 2021. "Salesforce Compensation and Two‐Sided Ambiguity: Robust Moral Hazard with Moment Information," Production and Operations Management, Production and Operations Management Society, vol. 30(9), pages 2944-2961, September.
    12. Soumyadip Ghosh & Henry Lam, 2019. "Robust Analysis in Stochastic Simulation: Computation and Performance Guarantees," Operations Research, INFORMS, vol. 67(1), pages 232-249, January.
    13. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    14. Ioana Popescu, 2007. "Robust Mean-Covariance Solutions for Stochastic Optimization," Operations Research, INFORMS, vol. 55(1), pages 98-112, February.
    15. Aleksandrina Goeva & Henry Lam & Huajie Qian & Bo Zhang, 2019. "Optimization-Based Calibration of Simulation Input Models," Operations Research, INFORMS, vol. 67(5), pages 1362-1382, September.
    16. Viet Anh Nguyen & Fan Zhang & Shanshan Wang & Jose Blanchet & Erick Delage & Yinyu Ye, 2021. "Robustifying Conditional Portfolio Decisions via Optimal Transport," Papers 2103.16451, arXiv.org, revised Apr 2024.
    17. Yan Chen & Ward Whitt, 2022. "Applying optimization theory to study extremal GI/GI/1 transient mean waiting times," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 197-220, August.
    18. Li, Zhaolin, 2021. "Robust Moral Hazard with Distributional Ambiguity," Working Papers BAWP-2021-01, University of Sydney Business School, Discipline of Business Analytics.
    19. J. Eric Bickel & James E. Smith, 2006. "Optimal Sequential Exploration: A Binary Learning Model," Decision Analysis, INFORMS, vol. 3(1), pages 16-32, March.
    20. Bernhard Kasberger, 2022. "An Equilibrium Model of the First-Price Auction with Strategic Uncertainty: Theory and Empirics," Papers 2202.07517, arXiv.org, revised Mar 2022.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:116:y:2006:i:5:p:724-756. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.