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Automated Estimation of Extreme Steady-State Quantiles via the Maximum Transformation

Published: 14 November 2017 Publication History

Abstract

We present Sequem, a sequential procedure that delivers point and confidence-interval (CI) estimators for extreme steady-state quantiles of a simulation-generated process. Because it is specified completely, Sequem can be implemented directly and applied automatically. The method is an extension of the Sequest procedure developed by Alexopoulos et al. in 2014 to estimate nonextreme steady-state quantiles. Sequem exploits a combination of batching, sectioning, and the maximum transformation technique to achieve the following: (i) reduction in point-estimator bias arising from the simulation’s initial condition or from inadequate simulation run length; and (ii) adjustment of the CI half-length to compensate for the effects of skewness or autocorrelation on intermediate quantile point estimators computed from nonoverlapping batches of observations. Sequem’s CIs are designed to satisfy user-specified requirements concerning coverage probability and absolute or relative precision. In an experimental evaluation based on seven processes selected to stress-test the procedure, Sequem exhibited uniformly good performance.

References

[1]
J. Abate and W. Whitt. 2006. A unified framework for numerically inverting Laplace transforms. INFORMS J. Comput. 18, 4 (2006), 408--421.
[2]
C. Alexopoulos, D. Goldsman, A. Mokashi, R. Nie, Q. Sun, K.-W. Tien, and J. R. Wilson. 2014. Sequest: A sequential procedure for estimating steady-state quantiles. In Proceedings of the 2014 Winter Simulation Conference, A. Tolk, S. Y. Diallo, I. O. Ryzhov, L. Yilmaz, S. Buckley, and J. A. Miller (Eds.). Institute of Electrical and Electronics Engineers, Piscataway, NJ, 662--673.
[3]
C. Alexopoulos, D. Goldsman, A. C. Mokashi, K.-W. Tien, and J. R. Wilson. 2016. Sequest: A sequential procedure for estimating quantiles in steady-state simulations. Operations Research (2016), In revision. Retrieved on May 25, 2017 from http://www4.ncsu.edu/∼jwilson/files/alexopoulos16or.pdf.
[4]
C. Alexopoulos, D. Goldsman, A. C. Mokashi, and J. R. Wilson. 2015. Sequem: Estimating extreme steady-state quantiles via the maximum transformation. In Proceedings of the 2015 Winter Simulation Conference, L. Yilmaz, W. K. V. Chan, I. Moon, T. M. K. Roeder, C. Macal, and M. D. Rossetti (Eds.). Institute of Electrical and Electronics Engineers, Piscataway, NJ, 562--574.
[5]
C. Alexopoulos, D. Goldsman, and J. R. Wilson. 2012. A new perspective on batched quantile estimation. In Proceedings of the 2012 Winter Simulation Conference, C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher (Eds.). Institute of Electrical and Electronics Engineers, Piscataway, NJ, 190--200.
[6]
S. Asmussen and P. W. Glynn. 2007. Stochastic Simulation: Algorithms and Analysis. Springer Science+Business Media, New York.
[7]
J. M. Bekki, J. W. Fowler, G. T. Mackulak, and B. L. Nelson. 2010. Indirect cycle time quantile estimation using the Cornish--Fisher expansion. IIE Trans. 42, 1 (2010), 31--44.
[8]
P. Billingsley. 1999. Convergence of Probability Measures (2nd ed.). John Wiley 8 Sons, New York.
[9]
E. J. Chen and W. D. Kelton. 2006. Quantile and tolerance-interval estimation in simulation. European J. Operat. Res. 168 (2006), 520--540.
[10]
E. J. Chen and W. D. Kelton. 2008. Estimating steady-state distributions via simulation-generated histograms. Comput. Operat. Res. 35, 4 (2008), 1003--1016.
[11]
H. Drees. 2003. Extreme quantile estimation of dependent data, with applications to finance. Bernoulli 9, 1 (2003), 617--647.
[12]
E. J. Hannan. 1960. Time Series Analysis. Chapman and Hall, London.
[13]
P. Heidelberger and P. A. W. Lewis. 1984. Quantile estimation in dependent sequences. Operat. Res. 32 (1984), 185--209.
[14]
D. L. Iglehart. 1976. Simulating stable stochastic systems, VI: Quantile estimation. J. Assoc. Comput. Mach. 23 (1976), 347--360.
[15]
R. Jain and I. Chlamtac. 1985. The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations. Commun. ACM 28, 10 (1985), 1076--1085.
[16]
X. Jin, M. C. Fu, and X. Xiong. 2003. Probabilistic error bounds for simulation quantile estimators. Manage. Sci. 49 (2003), 230--246.
[17]
L. Kleinrock. 1975. Queueing Systems, Volume I: Theory. Wiley, New York.
[18]
M. Kohler, A. Krzyżak, and H. Walk. 2014. Nonparametric recursive quantile estimation. Stat. Prob. Lett. 93 (2014), 102--107.
[19]
E. K. Lada, N. M. Steiger, and J. R. Wilson. 2006. Performance evaluation of recent procedures for steady-state simulation analysis. IIE Trans. 38 (2006), 711--727.
[20]
A. M. Law and J. S. Carson. 1979. A sequential procedure for determining the length of a steady-state simulation. Operat. Res. 27 (1979), 1011--1025.
[21]
J. C. Liechty, D. K. Lin, and J. P. McDermott. 2003. Single-pass low-storage arbitrary quantile estimation for massive datasets. Stat. Comput. 13 (2003), 91–100.
[22]
A. J. McNeil and R. Frey. 2000. Estimation of tail-related risk measures for heteroscedastic financial time-series: An extreme value approach. J. Empir. Finance 7 (2000), 271--300.
[23]
D. F. Muñoz. 2010. On the validity of the batch quantile method for Markov chains. Operat. Res. Lett. 38, 3 (2010), 223--226.
[24]
K. E. E. Raatikainen. 1987. Simultaneous estimation of several percentiles. Simulation 49 (1987), 159--163.
[25]
K. E. E. Raatikainen. 1990. Sequential procedure for simultaneous estimation of several percentiles. Trans. Soc. Comput. Simul. 7, 1 (1990), 21--44.
[26]
A. F. Seila. 1982a. A batching approach to quantile estimation in regenerative simulations. Manage. Sci. 28, 5 (1982), 573--581.
[27]
A. F. Seila. 1982b. Estimation of percentiles in discrete event simulation. Simulation 6 (1982), 193--200.
[28]
P. K. Sen. 1972. On the Bahadur representation of sample quantiles for sequences of &phis;-mixing random variables. J. Multivar. Anal. 2, 1 (1972), 77--95.
[29]
R. J. Serfling. 1980. Approximation Theorems of Mathematical Statistics. John Wiley 8 Sons, New York.
[30]
A. Tafazzoli and J. R. Wilson. 2011. Skart: A skewness- and autoregression-adjusted batch means procedure for simulation analysis. IIE Trans. 43, 2 (2011), 110--128.
[31]
A. Tafazzoli, J. R. Wilson, E. K. Lada, and N. M. Steiger. 2011. Performance of Skart: A skewness- and autoregression-adjusted batch-means procedure for simulation analysis. INFORMS J. Comput. 23 (2011), 297--314.
[32]
J. von Neumann. 1941. Distribution of the ratio of the mean square successive difference to the variance. Ann. Math. Stat. 12, 4 (1941), 367--395.
[33]
R. J. Wang and P. W. Glynn. 2016. On the marginal standard error rule and the testing of initial transient deletion methods. ACM Trans. Model. Comput. Simul. 27, 1 (2016), Article 1.
[34]
W. B. Wu. 2005. On the Bahadur representation of sample quantiles for dependent sequences. Ann. Stat. 33, 4 (2005), 1924--1963.
[35]
V. Yaroslavskiy. 2009. Dual pivot quicksort. Retrieved on October 10, 2016 from http://codeblab.com/wp-content/uploads/2009/09/DualPivotQuicksort.pdf.

Cited By

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  • (2024)SQSTS: A sequential procedure for estimating steady-state quantiles using standardized time seriesJournal of Simulation10.1080/17477778.2024.2362438(1-23)Online publication date: 14-Nov-2024
  • (2022)A Sequential Method for Estimating Steady-State Quantiles Using Standardized Time SeriesProceedings of the Winter Simulation Conference10.5555/3586210.3586217(73-84)Online publication date: 11-Dec-2022
  • (2022)Overlapping Batch Confidence Regions on the Steady-State Quantile VectorProceedings of the Winter Simulation Conference10.5555/3586210.3586213(25-36)Online publication date: 11-Dec-2022
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    cover image ACM Transactions on Modeling and Computer Simulation
    ACM Transactions on Modeling and Computer Simulation  Volume 27, Issue 4
    October 2017
    158 pages
    ISSN:1049-3301
    EISSN:1558-1195
    DOI:10.1145/3155315
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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    Publication History

    Published: 14 November 2017
    Accepted: 01 June 2017
    Revised: 01 June 2017
    Received: 01 August 2015
    Published in TOMACS Volume 27, Issue 4

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    Author Tags

    1. Quantile estimation
    2. maximum transformation method
    3. method of batching
    4. method of sectioning
    5. sequential procedure
    6. steady-state simulation

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    Cited By

    View all
    • (2024)SQSTS: A sequential procedure for estimating steady-state quantiles using standardized time seriesJournal of Simulation10.1080/17477778.2024.2362438(1-23)Online publication date: 14-Nov-2024
    • (2022)A Sequential Method for Estimating Steady-State Quantiles Using Standardized Time SeriesProceedings of the Winter Simulation Conference10.5555/3586210.3586217(73-84)Online publication date: 11-Dec-2022
    • (2022)Overlapping Batch Confidence Regions on the Steady-State Quantile VectorProceedings of the Winter Simulation Conference10.5555/3586210.3586213(25-36)Online publication date: 11-Dec-2022
    • (2022)Overlapping Batch Confidence Regions on the Steady-State Quantile Vector2022 Winter Simulation Conference (WSC)10.1109/WSC57314.2022.10015372(25-36)Online publication date: 11-Dec-2022
    • (2022)A Sequential Method for Estimating Steady-State Quantiles Using Standardized Time Series2022 Winter Simulation Conference (WSC)10.1109/WSC57314.2022.10015283(73-84)Online publication date: 11-Dec-2022
    • (2020)Steady-state quantile estimation using standardized time seriesProceedings of the Winter Simulation Conference10.5555/3466184.3466216(289-300)Online publication date: 14-Dec-2020
    • (2020)Steady-State Quantile Estimation Using Standardized Time Series2020 Winter Simulation Conference (WSC)10.1109/WSC48552.2020.9384130(289-300)Online publication date: 14-Dec-2020
    • (2020)A Tutorial on Quantile Estimation via Monte CarloMonte Carlo and Quasi-Monte Carlo Methods10.1007/978-3-030-43465-6_1(3-30)Online publication date: 2-May-2020
    • (2019)Sequential estimation of steady-state quantilesProceedings of the Winter Simulation Conference10.5555/3400397.3400704(3774-3785)Online publication date: 8-Dec-2019
    • (2019)SequestOperations Research10.1287/opre.2018.182967:4(1162-1183)Online publication date: 28-Jun-2019
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