Variance reduction for quantile estimates in simulations via nonlinear controls

References

• Beale , E. 1985 . Regression: A Bridge Between Analysis and Simulation . The Statis-tician , 34 : 141 – 154 .
   Web of Science ®Google Scholar
• Breiman , L. and Friedman , J. H. 1985 . Estimating Optimal Transformations for Multiple Regression and Correlation . Journal of the American Statistical Association , 80 ( 391 ) September : 580 – 619 .
   Web of Science ®Google Scholar
• Chambers , J. M. , Cleveland , W. S. , Kleiner , B. and Tukey , P. A. 1983 . Graphical Methods for Data Analysis , Duxbury Press .
   Google Scholar
• David , H. A. 1970 . Order Statistics , John Wiley & Sons, Inc .
   Google Scholar
• Efron , B. and Gong , G. 1983 . A Leisurely Look at the Bootstrap, the Jackknife and Cross-validation . The American Statistician , 37 ( 1 ) February : 36 – 48 .
   Web of Science ®Google Scholar
• Gallant , A. R. 1987 . Nonlinear Regression , John Wiley & Sons .
   Google Scholar
• Glynn , P. W. and Whitt , W. 1989 . Indirect Estimation via L = λlW . Operations Research , 37 ( 1 ) 82 – 103 .
   Web of Science ®Google Scholar
• Heidelberger , P. and Lewis , P. A. W. 1981 . Regression-adjusted Estimates for Regenerative Simulations, with Graphics . Communications of the ACM , 24 ( 4 ) April : 260 – 273 .
   Web of Science ®Google Scholar
• Hsu , J. C. and Nelson , B. L. 1987 . “ Control Variates for Quantile Estimation ” . In In Proceedings of the 1987 Winter Simulation Conference Edited by: Thesen , A. , Grant , H. and Kelton , W. D. 342 – 346 .
   Google Scholar
• Kendall , M. and Stuart , A. 1977 . The Advanced Theory of Statistics , Vol. 1 , Macmillan .
   Google Scholar
• Lancaster , H. 0. 1966 . Kolmogorov's Remark on the Hotelling Canonical Correlation . Biometrika , 53 ( 3 and 4 ) : 585 – 590 .
   Google Scholar
• Lavenberg , S. S. , Moeller , T. L. and Welch , P. D. 1982 . Statistical Results on Control Variables with Application to Queueing Network Simulation . Operations Research , 30 ( 1 ) January and February : 182 – 202 .
   Web of Science ®Google Scholar
• Lewis , P. A. W. and Orav , J. 1989 . “ Simulation Methodology for Statisticians ” . In Operations Analysts, and Engineers , Vol. 1 , Wadsworth & Brooks/Cole .
   Google Scholar
• Lewis , P. A. W. , Ressler , R. L. and Wood , R. K. 1989 . Variance Reduction using Nonlinear Controls and Transformations . Communications in Statistics, Part B , 18 ( 2 ) : 655 – 672 .
   Web of Science ®Google Scholar
• Miller , R. G. 1974 . The Jackknife - A Review . Biometrika , 61 ( 1 ) : 1 – 15 .
   Web of Science ®Google Scholar
• Mood , A. M. , Graybill , F. A. and Boes , D. C. 1974 . Introduction to the Theory of Statistics , McGraw Hill .
   Google Scholar
• Nelson, B. L., Control- Variate Remedies, Department of Industrial and Systems Engineering, The Ohio State University, Report 1988-004, October 1988
   Google Scholar
• Rubinstein , R. Y. and Marcus , R. 1985 . Efficiency of Multivariate Control Variates in Monte Carlo Simulation . Operations Research , 33 ( 3 ) May-June : 661 – 667 .
   Web of Science ®Google Scholar
• Seila , A. F. 1982 . A Batching Approach to Quantile Estimation in Regenerative Simulation . Management Science , 28 ( 3 ) May-June : 573 – 581 .
   Web of Science ®Google Scholar
• Serfling , R. J. 1980 . Approximation Theorems of Mathematical Statistics , New York : Wiley .
   Google Scholar
• Tocher , K. D. 1963 . The Art of Simulation , The English Universities Press, Ltd .
   Google Scholar
• Weiss , L. 1964 . On the Asymptotic Joint Normality of Quantiles from a Multivariate Distribution . Journal of Research of the National Bureau of Standards , 68B ( 2 ) April-June : 65 – 66 .
   Google Scholar