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Technical Note—On Estimating Quantile Sensitivities via Infinitesimal Perturbation Analysis

Author

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  • Guangxin Jiang

    (Department of Mathematics, Tongji University, Shanghai, 200092, China)

  • Michael C. Fu

    (Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

Abstract

Hong (2009) [Hong LJ (2009) Estimating quantile sensitivities. Oper. Res. 57(1):118-130.] introduced a general framework based on probability sensitivities and a conditional expectation relationship for estimating quantile sensitivities by infinitesimal perturbation analysis (IPA). We present an alternative more direct derivation of the IPA estimators that leads to simplified proofs for strong consistency and convergence rate of the unbatched estimator, and strong consistency and a central limit theorem for the batched estimator.

Suggested Citation

  • Guangxin Jiang & Michael C. Fu, 2015. "Technical Note—On Estimating Quantile Sensitivities via Infinitesimal Perturbation Analysis," Operations Research, INFORMS, vol. 63(2), pages 435-441, April.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:2:p:435-441
    DOI: 10.1287/opre.2015.1356
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    References listed on IDEAS

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    1. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, September.
    2. Rajan Suri & Michael A. Zazanis, 1988. "Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue," Management Science, INFORMS, vol. 34(1), pages 39-64, January.
    3. Guangwu Liu & Liu Jeff Hong, 2009. "Kernel estimation of quantile sensitivities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 511-525, September.
    4. L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    5. L. Jeff Hong & Guangwu Liu, 2009. "Simulating Sensitivities of Conditional Value at Risk," Management Science, INFORMS, vol. 55(2), pages 281-293, February.
    6. Michael C. Fu & L. Jeff Hong & Jian-Qiang Hu, 2009. "Conditional Monte Carlo Estimation of Quantile Sensitivities," Management Science, INFORMS, vol. 55(12), pages 2019-2027, December.
    7. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
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    Citations

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    Cited by:

    1. Jiaqiao Hu & Yijie Peng & Gongbo Zhang & Qi Zhang, 2022. "A Stochastic Approximation Method for Simulation-Based Quantile Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2889-2907, November.
    2. Yijie Peng & Chun-Hung Chen & Michael C. Fu & Jian-Qiang Hu & Ilya O. Ryzhov, 2021. "Efficient Sampling Allocation Procedures for Optimal Quantile Selection," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 230-245, January.
    3. He, Zhijian, 2022. "Sensitivity estimation of conditional value at risk using randomized quasi-Monte Carlo," European Journal of Operational Research, Elsevier, vol. 298(1), pages 229-242.
    4. Peter W. Glynn & Yijie Peng & Michael C. Fu & Jian-Qiang Hu, 2021. "Computing Sensitivities for Distortion Risk Measures," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1520-1532, October.
    5. Yijie Peng & Michael C. Fu & Bernd Heidergott & Henry Lam, 2020. "Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling," Operations Research, INFORMS, vol. 68(6), pages 1896-1912, November.

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