Sequest: A Sequential Procedure for Estimating Quantiles in Steady-State Simulations
Published Online:28 Jun 2019https://doi.org/10.1287/opre.2018.1829
References
- (2006) A unified framework for numerically inverting Laplace transforms. INFORMS J. Comput. 18(4):408–421.Link, Google Scholar
- (2012) A new perspective on batched quantile estimation. Laroque C, Himmelspach J, Pasupathy R, Rose O, Uhrmacher AM, eds. Proc. 2012 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 190–200.Crossref, Google Scholar
- (2017) Automated estimation of extreme steady-state quantiles via the maximum transformation. ACM Trans. Model. Comput. Simulation 27(4):22:1–22:29.Crossref, Google Scholar
- (2016) SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series. IIE Trans. 48(9):864–880.Crossref, Google Scholar
- (2015) Sequem: Estimating extreme steady-state quantiles via the maximum transformation. Yilmaz L, Chan WKV, Moon I, Roeder TMK, Macal C, Rossetti MD, eds. Proc. 2015 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 562–574.Crossref, Google Scholar
- (2018) Availability of the Sequest software for Windows and Linux. Accessed November 9, 2018, www4.ncsu.edu/∼jwilson/files/sequest-availability.pdf.Google Scholar
- (2014) Sequest: A sequential procedure for estimating steady-state quantiles. Tolk A, Diallo SY, Ryzhov IO, Yilmaz L, Buckley S, Miller JA, eds. Proc. 2014 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 662–673.Crossref, Google Scholar
- (2007) Stochastic Simulation: Algorithms and Analysis (Springer Science + Business Media, New York).Crossref, Google Scholar
- (1998) Correlation-induction techniques for estimating quantiles in simulation experiments. Oper. Res. 46(4):574–591.Link, Google Scholar
- (1966) A note on quantiles in large samples. Ann. Math. Statist. 37(3):577–580.Crossref, Google Scholar
- (2009) Simulation-based cycle-time quantile estimation in manufacturing settings employing non-FIFO dispatching policies. J. Simulation 3(2):69–83.Crossref, Google Scholar
- (2010) Indirect cycle time quantile estimation using the Cornish–Fisher expansion. IIE Trans. 42(1):31–44.Crossref, Google Scholar
- (1968) Convergence of Probability Measures (John Wiley & Sons, New York).Google Scholar
- (1995) Probability and Measure, 3rd ed. (John Wiley & Sons, New York).Google Scholar
- (1999) Convergence of Probability Measures, 2nd ed. (John Wiley & Sons, New York).Crossref, Google Scholar
- (1986) Generalized autoregressive conditional heteroskedasticity. J. Econom. 31(3):307–327.Crossref, Google Scholar
- (2005) Basic properties of strong mixing conditions. A survey and some open questions. Probab. Surveys 2:107–144.Crossref, Google Scholar
- (2006) Quantile and tolerance-interval estimation in simulation. Eur. J. Oper. Res. 168(2):520–540.Crossref, Google Scholar
- (2008) Estimating steady-state distributions via simulation-generated histograms. Comput. Oper. Res. 35(4):1003–1016.Crossref, Google Scholar
- (1968) The serial correlation coefficients of waiting times in a stationary single server queue. J. Australian Math. Soc. 8(4):683–699.Crossref, Google Scholar
- (2003) Order Statistics, 2nd ed. (John Wiley & Sons, New York).Crossref, Google Scholar
- (1973) A note on empirical processes of strong-mixing sequences. Ann. Probab. 1(5):870–875.Crossref, Google Scholar
- (2017) Quantile estimation with Latin hypercube sampling. Oper. Res. 65(6):1678–1695.Link, Google Scholar
- (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50(4):987–1007.Crossref, Google Scholar
- (1960) The percentile points of distributions having known cumulants. Technometrics 2(2):209–225.Crossref, Google Scholar
- (1972) Bias considerations in simulation experiments. Oper. Res. 20(4):785–790.Link, Google Scholar
- (2004) Monte Carlo Methods in Financial Engineering (Springer-Verlag, New York).Crossref, Google Scholar
- (1984) Quantile estimation in dependent sequences. Oper. Res. 32(1):185–209.Link, Google Scholar
- (2008) Factory Physics, 3rd ed. (McGraw-Hill/Irwin, New York).Google Scholar
- (1975) Simulating stable stochastic systems, V: Comparison of ratio estimators. Naval Res. Logist. Quart. 22(3):553–565.Crossref, Google Scholar
- (1976) Simulating stable stochastic systems, VI: Quantile estimation. J. Assoc. Comput. Machinery 23(2):347–360.Crossref, Google Scholar
- (1985) The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations. Comm. ACM 28(10):1076–1085.Crossref, Google Scholar
- (2003) Probabilistic error bounds for simulation quantile estimators. Management Sci. 49(2):230–246.Link, Google Scholar
- (1998) Comparing measures of sample skewness and kurtosis. Statistician 47(part 1):183–189.Google Scholar
- (1975) Queueing Systems, Volume I: Theory (John Wiley & Sons, New York).Google Scholar
- (2006) Performance evaluation of recent procedures for steady-state simulation analysis. IIE Trans. 38(9):711–727.Crossref, Google Scholar
- (2007) Performance of a wavelet-based procedure for steady-state simulation analysis. INFORMS J. Comput. 19(2):150–160.Link, Google Scholar
- (1979) A sequential procedure for determining the length of a steady-state simulation. Oper. Res. 27(5):1011–1025.Link, Google Scholar
- (2002) Recent theoretical results for time series models with GARCH errors. J. Econom. Surveys 16(3):245–269.Crossref, Google Scholar
- (1963) The variation of certain speculative prices. J. Bus. 36(4):394–419.Crossref, Google Scholar
- (2010) On the validity of the batch quantile method for Markov chains. Oper. Res. Lett. 38(3):223–226.Crossref, Google Scholar
- (2015) A note on bias and mean squared error in steady-state quantile estimation. Oper. Res. Lett. 43(4):374–377.Crossref, Google Scholar
- (1994) Numerical computation of response time distributions using stochastic reward nets. Ann. Oper. Res. 48(2):155–184.Crossref, Google Scholar
- (2008) The MORE plot: Displaying measures of risk & error from simulation output. Mason SJ, Hill RR, Mönch L, Rose O, Jefferson T, Fowler JW, eds. Proc. 2008 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 413–416.Crossref, Google Scholar
- (1982) Random Coefficient Autoregressive Models: An Introduction (Springer, New York).Crossref, Google Scholar
- (1987) Simultaneous estimation of several percentiles. Simulation 49(4):159–163.Crossref, Google Scholar
- (1990) Sequential procedure for simultaneous estimation of several percentiles. Trans. Soc. Comput. Simulation 7(1):21–44.Google Scholar
- (1961) Delays for the last-come first-served service and the busy period. Bell System Tech. J. 40(3):785–793.Crossref, Google Scholar
- (1982a) A batching approach to quantile estimation in regenerative simulations. Management Sci. 28(5):573–581.Link, Google Scholar
- (1982b) Estimation of percentiles in discrete event simulation. Simulation 39(6):193–200.Crossref, Google Scholar
- (1972) On the Bahadur representation of sample quantiles for sequences of ϕ-mixing random variables. J. Multivariate Anal. 2(1):77–95.Crossref, Google Scholar
- (1980) Approximation Theorems of Mathematical Statistics (John Wiley & Sons, New York).Crossref, Google Scholar
- (2007) Asymptotic spectral theory for nonlinear time series. Ann. Statist. 35(4):1773–1801.Crossref, Google Scholar
- (1996) Probability, 2nd ed. (Springer, New York).Crossref, Google Scholar
- (1995) Optimal mean-squared-error batch sizes. Management Sci. 41(1):110–123.Link, Google Scholar
- (2005) ASAP3: A batch means procedure for steady-state simulation analysis. ACM Trans. Model. Comput. Simulation 15(1):39–73.Crossref, Google Scholar
- (2011) Skart: A skewness- and autoregression-adjusted batch-means procedure for simulation analysis. IIE Trans. 43(2):110–128.Crossref, Google Scholar
- (2011a) N-Skart: A nonsequential skewness- and autoregression-adjusted batch-means procedure for simulation analysis. IEEE Trans. Automatic Control 56(2):254–264.Crossref, Google Scholar
- (2011b) Performance of Skart: A skewness- and autoregression-adjusted batch means procedure for simulation analysis. INFORMS J. Comput. 23(2):297–314.Link, Google Scholar
- (1990) Nonlinear Time Series: A Dynamical System Approach (Oxford University Press, New York).Google Scholar
- (2002) Probability and Statistics with Reliability, Queueing, and Computer Science Applications, 2nd ed. (John Wiley & Sons, New York).Google Scholar
- (1941) Distribution of the ratio of the mean square successive difference to the variance. Ann. Math. Statist. 12(4):367–395.Crossref, Google Scholar
- (2016) On the marginal standard error rule and the testing of initial transient deletion methods. ACM Trans. Model. Comput. Simulation 27(1):1:1–1:30.Crossref, Google Scholar
- (1983) The statistical analysis of simulation results. Lavenberg S, ed. Computer Performance Modeling Handbook (Academic Press, New York), 268–328.Google Scholar
- (1978) Evaluation of startup policies in simulation experiments. Simulation 31(3):79–89.Crossref, Google Scholar
- (2005) On the Bahadur representation of sample quantiles for dependent sequences. Ann. Statist. 33(4):1934–1963.Crossref, Google Scholar
- (2004) Limit theorems for iterated random functions. J. Appl. Probab. 41(2):425–436.Crossref, Google Scholar
- (2000) A central limit theorem for iterated random functions. J. Appl. Probab. 37(3):748–755.Crossref, Google Scholar
- (1995) The Bahadur representation of sample quantiles for sequences of strong mixing random variables. Statist. Probab. Lett. 24(4):299–304.Crossref, Google Scholar

