|
ABSTRACT
This tutorial discusses some statistical procedures for selecting the best of a number of competing systems. The term "best" may refer to that simulated system having, say, the largest expected value or the greatest likelihood of yielding a large observation. We describe various procedures for finding the best, some of which assume that the underlying observations arise from competing normal distributions, and some of which are essentially nonparametric in nature. In each case, we comment on how to apply the above procedures for use in simulations.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
| |
1
|
Bechhofer, R. E. 1954. A single-sample multiple decision procedure for ranking means of normal populations with known variances. Annals of Mathematical Statistics 25:16--39.
|
| |
2
|
Bechhofer, R. E., S. Elmaghraby, and N. Morse. 1959. A single-sample multiple decision procedure for selecting the multinomial event which has the highest probability. Annals of Mathematical Statistics 30:102--119.
|
| |
3
|
Bechhofer, R. E., and D. M. Goldsman. 1986. Truncation of the Bechhofer-Kiefer-Sobel sequential procedure for selecting the multinomial event which has the largest probability (II): Extended tables and an improved procedure. Communications in Statistics---Simulation and Computation B15:829--851.
|
| |
4
|
Bechhofer, R. E., T. J. Santner, and D. Goldsman. 1995. Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons. New York: John Wiley and Sons.
|
| |
5
|
Dunnett, C. W. 1989. Multivariate normal probability integrals with product correlation structure. Applied Statistics 38:564--579. Correction: 42:709.
|
| |
6
|
|
| |
7
|
|
| |
8
|
Goldsman, D., and B. L. Nelson. 1998. Comparing systems via simulation. Handbook of Simulation, ed. J. Banks, Chapter 8. New York: John Wiley and Sons.
|
| |
9
|
|
| |
10
|
Gupta, S. S. 1956. On a Decision Rule for a Problem in Ranking Means. Ph.D. Dissertation (Mimeo. Ser. No. 150). Institute of Statistics, University of North Carolina, Chapel Hill, North Carolina.
|
| |
11
|
Gupta, S. S. 1965. On some multiple decision (selection and ranking) rules. Technometrics 7:225--245.
|
| |
12
|
|
| |
13
|
Hsu, J. C. 1984. Constrained simultaneous confidence intervals for multiple comparisons with the best. Annals of Statistics 12:1136--1144.
|
| |
14
|
Hsu, J. C. 1996. Multiple Comparisons: Theory and Methods. New York: Chapman and Hall.
|
 |
15
|
|
| |
16
|
|
| |
17
|
Kim, S.-H., and B. L. Nelson. 2005a. Selecting the best system. To appear in Handbooks in Operations Research and Management Science: Simulation, ed. S. G. Henderson and B. L. Nelson, Chapter 17. Oxford: Elsevier Science.
|
| |
18
|
Kim, S.-H., and B. L. Nelson. 2005b. On the asymptotic validity of fully sequential selection procedures for steady-state simulation. To appear in Operations Research.
|
| |
19
|
|
| |
20
|
Matejcik, F. J., and B. L. Nelson. 1995. Two-stage multiple comparisons with the best for computer simulation. Operations Research 43:633--640.
|
| |
21
|
Miller, J. O., B. L. Nelson, and C. H. Reilly. Efficient multinomial selection in simulation. 1998. Naval Research Logistics 45:459--482.
|
| |
22
|
Nakayama, M. K. 1997. Multiple-comparison procedures for steady-state simulations. Annals of Statistics 25:2433--2450.
|
| |
23
|
|
| |
24
|
|
| |
25
|
|
| |
26
|
Paulson, E. 1964. A sequential procedure for selecting the population with the largest mean from k normal populations. Annals of Mathematical Statistics 35:174--180.
|
| |
27
|
Rinott, Y. 1978. On two-stage selection procedures and related probability-inequalities. Communications in Statistics---Theory and Methods A7:799--811.
|
| |
28
|
Wald, A. 1947. Sequential Analysis. New York: John Wiley.
|
| |
29
|
Wilcox, R. R. 1984. A table for Rinott's selection procedure. Journal of Quality Technology 16:97--100.
|
|