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Nonparametric estimation of the service time distribution in the discrete-time GI/G/∞ queue with partial information

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  • Schweer, Sebastian
  • Wichelhaus, Cornelia

Abstract

Estimation of the service time distribution in the discrete-time GI/G/∞-queue based solely on information on the arrival and departure processes is considered. The focus is put on the estimation approach via the so called “sequence of differences”. Existing results for this approach are substantially extended by proving a functional central limit theorem for the resultant estimator. Here, the underlying function space is taken to be the space of sequences converging to zero. The moving block bootstrap technique is considered for the estimation of the resultant covariance kernel and is shown to be applicable under mild additional conditions.

Suggested Citation

  • Schweer, Sebastian & Wichelhaus, Cornelia, 2015. "Nonparametric estimation of the service time distribution in the discrete-time GI/G/∞ queue with partial information," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 233-253.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:1:p:233-253
    DOI: 10.1016/j.spa.2014.09.003
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    References listed on IDEAS

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    1. Dragan Radulović, 2012. "Necessary and sufficient conditions for the moving blocks bootstrap central limit theorem of the mean," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 343-357.
    2. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    3. Peter Hall & Juhyun Park, 2004. "Nonparametric inference about service time distribution from indirect measurements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 861-875, November.
    4. N. Bingham & Susan Pitts, 1999. "Non-parametric Estimation for the M/G/∞ Queue," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(1), pages 71-97, March.
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    Cited by:

    1. Schweer, Sebastian & Wichelhaus, Cornelia, 2020. "Nonparametric estimation of the service time distribution in discrete-time queueing networks," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4643-4666.
    2. Sebastian Schweer, 2016. "A Goodness-of-Fit Test for Integer-Valued Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 77-98, January.
    3. Wenwen Li & Alexander Goldenshluger, 2024. "Adaptive minimax estimation of service time distribution in the $$M_t/G/\infty $$ M t / G / ∞ queue from departure data," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 81-123, October.
    4. Chaithanya Bandi & Eojin Han & Alexej Proskynitopoulos, 2024. "Robust Queue Inference from Waiting Times," Operations Research, INFORMS, vol. 72(2), pages 459-480, March.
    5. Azam Asanjarani & Yoni Nazarathy & Peter Taylor, 2021. "A survey of parameter and state estimation in queues," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 39-80, February.
    6. Antoine Djogbenou & Christian Gourieroux & Joann Jasiak & Paul Rilstone & Maygol Bandehali, 2022. "Transition model for coronavirus management," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(S1), pages 665-704, February.

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