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A Central Limit Theorem For Empirical Quantiles in the Markov Chain Setting

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Abstract

We provide a new proof of a central limit theorem for empirical quantiles in the positive-recurrent Markov process setting under conditions that are essentially tight. We also establish the validity of the method of nonoverlapping batch means with a fixed number of batches for interval estimation of the quantile. The conditions of these results are likely to be difficult to verify in practice, and so we also provide more easily verified sufficient conditions.

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Acknowledgements

We have benefited enormously from our association with Pierre L’Ecuyer over many years. We are grateful for Pierre’s scholarship, leadership and friendship. This work was partially supported by National Science Foundation grant CMMI-2035086.

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Authors and Affiliations

  1. Stanford University, Stanford, CA, USA

    Peter W. Glynn

  2. Cornell University, Ithaca, NY, USA

    Shane G. Henderson

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  1. Peter W. Glynn
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Correspondence to Shane G. Henderson .

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Editors and Affiliations

  1. Randwick, NSW, Australia

    Zdravko Botev

  2. NVIDIA, Berlin, Germany

    Alexander Keller

  3. University of Waterloo, Waterloo, ON, Canada

    Christiane Lemieux

  4. Rennes Bretagne-Atlantique, INRIA, Rennes Cedex, France

    Bruno Tuffin

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Glynn, P.W., Henderson, S.G. (2022). A Central Limit Theorem For Empirical Quantiles in the Markov Chain Setting. In: Botev, Z., Keller, A., Lemieux, C., Tuffin, B. (eds) Advances in Modeling and Simulation. Springer, Cham. https://doi.org/10.1007/978-3-031-10193-9_11

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