Stochastic kriging with biased sample estimates

ACM Transactions on Modeling and Computer Simulation

Volumn 24, Issue 2, 2014, Pages

  Chen, Xi ^a   Kim, Kyoung Kuk ^b  

^a VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

^b Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Metamodeling; Nested simulation; Optimal budget al.location; Simulation experimental design; Simulation output analysis; Simulation theory

Indexed keywords

BUDGET CONTROL; INTERPOLATION; OPTIMIZATION; RISK MANAGEMENT; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

METAMODELING; NESTED SIMULATION; OPTIMAL BUDGET AL.LOCATION; SIMULATION OUTPUT ANALYSIS; SIMULATION THEORY;

ESTIMATION;

EID: 84897431730     PISSN: 10493301     EISSN: 15581195     Source Type: Journal    
DOI: 10.1145/2567893     Document Type: Article

References (44)

1. Bruce E. Ankenman, Barry L. Nelson, and Jeremy Staum. 2010. Stochastic kriging for simulation metamodeling. Operations Research 58 (March-April 2010), 371-382.
2. Mark Broadie, Yiping Du, and Ciamac C. Moallemi. 2011. Efficient risk estimation via nested sequential simulation. Management Science 57 (June 2011), 1172-1194.
3. Xi Chen, Bruce E. Ankenman, and Barry L. Nelson. 2012a. The effects of common random numbers on stochastic kriging metamodels. ACM Transactions on Modeling and Computer Simulation 22 (July 2012), 7:1-7:20.
4. Xi Chen, Kyoung-Kuk Kim, and Barry L. Nelson. 2012b. Stochastic kriging for conditional value-at-risk and its sensitivities. In Proceedings of the 2012 Winter Simulation Conference, C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher (Eds.). 24:1-24:12.
5. Michael B. Gordy and Sandeep Juneja. 2010. Nested simulation in portfolio risk measurement. Management Science 56 (Oct. 2010), 1833-1848.
6. L. Jeff Hong and Guangwu Liu. 2009. Simulation sensitivities of conditional value at risk. Management Science 55 (Feb. 2009), 281-293.
7. Raghu N. Kackar and David A. Harville. 1984. Approximations for standard errors of estimators of fixed and random effects in mixed linear models. Journal of the American Statistical Association 79 (Dec. 1984), 853-862.
8. W. David Kelton. 1986. Replication splitting and variance for simulating discrete-parameter stochastic processes. Operations Research Letters 4 (April 1986), 275-279.
9. Marc C. Kennedy and Anthony O'Hagan. 2001. Bayesian calibration of computer models. Journal of the Royal Statistical Society 63, 425-464.
10. Jack P. C. Kleijnen. 2008. Design and Analysis of Simulation Experiments. Springer, New York, NY.
11. Hai Lan, Barry L. Nelson, and Jeremy Staum. 2010. A confidence interval procedure for expected shortfall risk measurement via two-level simulation. Operations Research 58 (Sept.-Oct. 2010), 1481-1490.
12. Ming Liu and Jeremy Staum. 2010. Stochastic kriging for efficient nested simulation of expected shortfall. Journal of Risk 12 (March 2010), 3-27.
13. Emanuel Parzen. 1962. Stochastic Processes. Holden-Day, CA.
14. Jerome Sacks, William J.Welch, Toby J. Mitchell, and Henry P.Wynn. 1989. Design and analysis of computer experiments. Statistical Science 4 (Nov. 1989), 409-423.
15. Thomas J. Santner, Brian J. Williams, and William I. Notz. 2003. The Design and Analysis of Computer Experiments. Springer, New York, NY.
16. Jaroslav Šimák. 2002. On experimental designs for derivative random fields. Ph.D. thesis. TUBergakademie Freiberg, Freiberg, Germany.
17. Jeremy Staum. 2009. Better simulation metamodeling: The why, what, and how of stochastic kriging. In Proceedings of the 2009 Winter Simulation Conference, M. D. Rossetti, R. R. Hill, B. Johansson, A. Dunkin, and R. G. Ingalls (Eds.). 119-133.
18. Yunpeng Sun, Daniel W. Apley, and Jeremy Staum. 2011. Efficient nested simulation for estimating the variance of a conditional expectation. Operations Research 59 (July-Aug. 2011), 998-1007.
19. A. Alexandre Trindade, Stan Uryasev, Alexander Shapiro, and Grigory Zrazhevsky. 2007. Financial prediction with constrained tail risk. Journal of Banking and Finance 31 (Nov. 2007), 3524-3538.
20. Ward Whitt. 2006. Analysis for design. In Simulation, S. G. Henderson and B. L. Nelson (Eds.). Elsevier, 381-413.
21. Daniel Zelterman. 1987. Estimating percentage points by simulation. Journal of Statistical Computation and Simulation 27, 107-125.
22. Dale L. Zimmerman and Noel Cressie. 1992. Mean squared prediction error in the spatial linear model with estimated covariance parameters. Annals of the Institute of Statistical Mathematics 44 (March 1992), 27-43.
23. Bruce E. Ankenman, Barry L. Nelson, and Jeremy Staum. 2010. Stochastic kriging for simulation metamodeling. Operations Research 58 (March-April 2010), 371-382.
24. Mark Broadie, Yiping Du, and Ciamac C. Moallemi. 2011. Efficient risk estimation via nested sequential simulation. Management Science 57 (June 2011), 1172-1194.
25. Xi Chen, Bruce E. Ankenman, and Barry L. Nelson. 2012a. The effects of common random numbers on stochastic kriging metamodels. ACM Transactions on Modeling and Computer Simulation 22 (July 2012), 7:1-7:20.
26. Xi Chen, Kyoung-Kuk Kim, and Barry L. Nelson. 2012b. Stochastic kriging for conditional value-at-risk and its sensitivities. In Proceedings of the 2012 Winter Simulation Conference, C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher (Eds.). 24:1-24:12.
27. Michael B. Gordy and Sandeep Juneja. 2010. Nested simulation in portfolio risk measurement. Management Science 56 (Oct. 2010), 1833-1848.
28. L. Jeff Hong and Guangwu Liu. 2009. Simulation sensitivities of conditional value at risk. Management Science 55 (Feb. 2009), 281-293.
29. Raghu N. Kackar and David A. Harville. 1984. Approximations for standard errors of estimators of fixed and random effects in mixed linear models. Journal of the American Statistical Association 79 (Dec. 1984), 853-862.
30. W. David Kelton. 1986. Replication splitting and variance for simulating discrete-parameter stochastic processes. Operations Research Letters 4 (April 1986), 275-279.
31. Marc C. Kennedy and Anthony O'Hagan. 2001. Bayesian calibration of computer models. Journal of the Royal Statistical Society 63, 425-464.
32. Jack P. C. Kleijnen. 2008. Design and Analysis of Simulation Experiments. Springer, New York, NY.
33. Hai Lan, Barry L. Nelson, and Jeremy Staum. 2010. A confidence interval procedure for expected shortfall risk measurement via two-level simulation. Operations Research 58 (Sept.-Oct. 2010), 1481-1490.
34. Ming Liu and Jeremy Staum. 2010. Stochastic kriging for efficient nested simulation of expected shortfall. Journal of Risk 12 (March 2010), 3-27.
35. Emanuel Parzen. 1962. Stochastic Processes. Holden-Day, CA.
36. Jerome Sacks, William J.Welch, Toby J. Mitchell, and Henry P.Wynn. 1989. Design and analysis of computer experiments. Statistical Science 4 (Nov. 1989), 409-423.
37. Thomas J. Santner, Brian J. Williams, and William I. Notz. 2003. The Design and Analysis of Computer Experiments. Springer, New York, NY.
38. Jaroslav Šimák. 2002. On experimental designs for derivative random fields. Ph.D. thesis. TUBergakademie Freiberg, Freiberg, Germany.
39. Jeremy Staum. 2009. Better simulation metamodeling: The why, what, and how of stochastic kriging. In Proceedings of the 2009 Winter Simulation Conference, M. D. Rossetti, R. R. Hill, B. Johansson, A. Dunkin, and R. G. Ingalls (Eds.). 119-133.
40. Yunpeng Sun, Daniel W. Apley, and Jeremy Staum. 2011. Efficient nested simulation for estimating the variance of a conditional expectation. Operations Research 59 (July-Aug. 2011), 998-1007.
41. A. Alexandre Trindade, Stan Uryasev, Alexander Shapiro, and Grigory Zrazhevsky. 2007. Financial prediction with constrained tail risk. Journal of Banking and Finance 31 (Nov. 2007), 3524-3538.
42. Ward Whitt. 2006. Analysis for design. In Simulation, S. G. Henderson and B. L. Nelson (Eds.). Elsevier, 381-413.
43. Daniel Zelterman. 1987. Estimating percentage points by simulation. Journal of Statistical Computation and Simulation 27, 107-125.
44. Dale L. Zimmerman and Noel Cressie. 1992. Mean squared prediction error in the spatial linear model with estimated covariance parameters. Annals of the Institute of Statistical Mathematics 44 (March 1992), 27-43.