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Control Variates for Quantile Estimation

Author

Listed:
  • Jason C. Hsu

    (Department of Statistics, Ohio State University, Columbus, Ohio 43210-1271)

  • Barry L. Nelson

    (Department of Industrial and Systems Engineering, Ohio State University, Columbus, Ohio 43210)

Abstract

New point and interval estimators for quantiles that employ a control variate are introduced. The properties of these estimators do not depend on the usual assumption of joint normality between the random variable of interest and the control. Illustrative examples for queueing and stochastic activity network models are given. In those examples, the new estimators are superior to the standard estimator in terms of the mean squared error of the point estimator and the length of the confidence interval.

Suggested Citation

  • Jason C. Hsu & Barry L. Nelson, 1990. "Control Variates for Quantile Estimation," Management Science, INFORMS, vol. 36(7), pages 835-851, July.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:7:p:835-851
    DOI: 10.1287/mnsc.36.7.835
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    Citations

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    Cited by:

    1. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    2. Kenneth W. Bauer & James R. Wilson, 1992. "Control‐variate selection criteria," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 307-321, April.
    3. 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.
    4. Hui Dong & Marvin K. Nakayama, 2017. "Quantile Estimation with Latin Hypercube Sampling," Operations Research, INFORMS, vol. 65(6), pages 1678-1695, December.
    5. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Estimating risks of option books using neural-SDE market models," Papers 2202.07148, arXiv.org.
    6. Chen, E. Jack & Kelton, W. David, 2006. "Quantile and tolerance-interval estimation in simulation," European Journal of Operational Research, Elsevier, vol. 168(2), pages 520-540, January.
    7. Xi Chen & Kyoung-Kuk Kim, 2016. "Efficient VaR and CVaR Measurement via Stochastic Kriging," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 629-644, November.
    8. Timothy C. Hesterberg & Barry L. Nelson, 1998. "Control Variates for Probability and Quantile Estimation," Management Science, INFORMS, vol. 44(9), pages 1295-1312, September.
    9. Huei-Wen Teng, 2023. "Importance Sampling for Calculating the Value-at-Risk and Expected Shortfall of the Quadratic Portfolio with t-Distributed Risk Factors," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1125-1154, October.
    10. Xing Jin & Michael C. Fu & Xiaoping Xiong, 2003. "Probabilistic Error Bounds for Simulation Quantile Estimators," Management Science, INFORMS, vol. 49(2), pages 230-246, February.

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