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Quantiles on Stream: An Application to Monte Carlo Simulation

Author

Listed:
  • Wang Wei

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing100190, China)

  • Ching Wai-Ki

    (Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Hong Kong, China)

  • Wang Shouyang

    (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing100190, China)

  • Yu Lean

    (School of Economics and Management, Beijing University of Chemical Technology, Beijing100029, China)

Abstract

Monte Carlo simulation is an efficient method to estimate quantile. However, it becomes a serious problem when a huge sample size is required but the memory is insufficient. In this paper, we apply the stream quantile algorithm to Monte Carlo simulation in order to estimate quantile with limited memory. A rigorous theoretical analysis on the properties of the ϵn-approximate quantile is proposed in this paper. We prove that if ϵn = o(n-1/2), then the ϵn-approximate α-quantile computed by any deterministic stream quantile algorithm is a consistent and asymptotically normal estimator of the true quantile qα. We suggest setting ϵn = 1/(n1/2 log10n) in practice. Two deterministic stream quantile algorithms, including of GK algorithm and ZW algorithm, are employed to illustrate the performance of the ϵn-approximate quantile. The numerical example shows that the deterministic stream quantile algorithm can provide desired estimator of the true quantile with less memory.

Suggested Citation

  • Wang Wei & Ching Wai-Ki & Wang Shouyang & Yu Lean, 2016. "Quantiles on Stream: An Application to Monte Carlo Simulation," Journal of Systems Science and Information, De Gruyter, vol. 4(4), pages 334-342, August.
    • Handle: RePEc:bpj:jossai:v:4:y:2016:i:4:p:334-342:n:4
    DOI: 10.21078/JSSI-2016-334-09
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    References listed on IDEAS

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    1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, November.
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