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Multinomial selection for comparison with a standard. (English) Zbl 1219.62037
Summary: The multinomial selection problem is considered under the formulation of comparison with a standard, where each system is required to be compared to a single system, referred to as a “standard,” as well as to other alternative systems. The goal is to identify systems that are better than the standard, or to retain the standard when it is equal to or better than the other alternatives in terms of the probability to generate the largest or smallest performance measure. We derive new multinomial selection procedures for comparison with a standard to be applied in different scenarios, including exact small-sample procedure and approximate large-sample procedure. Empirical results and the proof are presented to demonstrate the statistical validity of our procedures. The tables of the procedure parameters and the corresponding exact probability of correct selection are also provided.
MSC:
62F07 Statistical ranking and selection procedures
65C60 Computational problems in statistics (MSC2010)
90B50 Management decision making, including multiple objectives
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[1] Adelman , D. , Goldsman , D. M. , Auclair , P. , Swain , J. J. ( 1993 ). Multinomial selection procedures for use in simulations .Proceedings of the 1993 Winter Simulation Conference, pp. 378 – 385 . · doi:10.1109/WSC.1993.718075
[2] Bechhofer R. E., American Journal of Mathematical and Management Sciences 11 pp 309– (1991) · Zbl 0774.62084 · doi:10.1080/01966324.1991.10737314
[3] Bechhofer R. E., The Annals of Mathematical Statistics 30 (1) pp 102– (1959) · Zbl 0218.62064 · doi:10.1214/aoms/1177706362
[4] Bechhofer R. E., Communications in Statistics–Simulation and Computation 14 pp 283– (1985) · Zbl 0583.62023 · doi:10.1080/03610918508812441
[5] Bechhofer R. E., Communications in Statistics–Simulation and Computation 15 pp 829– (1986) · Zbl 0601.62034 · doi:10.1080/03610918608812545
[6] Bechhofer R. E., Sequential Identfication and Ranking Procedures (with Special Reference to Koopman–Darmois Populations) (1968) · Zbl 0208.44601
[7] Bechhofer R. E., Annals of Mathematical Statistics 29 pp 325– (1958) · doi:10.1214/aoms/1177706739
[8] Bechhofer R. E., Journal of the American Statistical Association 73 pp 385– (1978)
[9] Bose M., Sequential Analysis 20 pp 165– (2001) · Zbl 0985.62020 · doi:10.1081/SQA-100106054
[10] Chen E. J., Discrete Event Dynamic Systems 16 pp 385– (2006) · Zbl 1306.93004 · doi:10.1007/s10626-006-9328-9
[11] Chen P., British Journal of Mathematical and Statistical Psychology 44 pp 403– (1991) · doi:10.1111/j.2044-8317.1991.tb00971.x
[12] Gupta S. S., Sankhyā 28 pp 1– (1967)
[13] Kesten H., Annals of Mathematical Statistics 30 pp 120– (1959) · Zbl 0218.62017 · doi:10.1214/aoms/1177706363
[14] Kim S.-H., ACM Transactions on Modeling and Computer Simulation 15 pp 155– (2005) · Zbl 05458234 · doi:10.1145/1060576.1060579
[15] Kim S.-H., Handbooks in Operations Research and Management Science: Simulation 13 pp 501– (2006)
[16] Kim , S.H. , Nelson , B. L. ( 2007 ). Recent advances in ranking and selection .Proceedings of the 2007 Winter Simulation Conference.Institute of Electrical and Electronic Engineers , Piscataway , NJ , pp. 162 – 172 .
[17] Law A., Simulation Modeling and Analysis (2007)
[18] Miller J. O., Naval Research Logistics 45 pp 459– (1998) · Zbl 0940.90062 · doi:10.1002/(SICI)1520-6750(199808)45:5<459::AID-NAV2>3.0.CO;2-2
[19] Miller J. O., Naval Research Logistics 49 pp 341– (2002) · Zbl 0993.62019 · doi:10.1002/nav.10019
[20] Nelson B. L., Management Science 47 pp 449– (2001) · Zbl 06007281 · doi:10.1287/mnsc.47.3.449.9778
[21] Paulson E., Annals of Mathematical Statistics 23 pp 239– (1952) · Zbl 0046.36002 · doi:10.1214/aoms/1177729440
[22] Tong T. L., Probability Inequalites in Multivariate Distributions (1980)
[23] Tong T. L., The Multivariate Normal Distribution (1990) · Zbl 0689.62036 · doi:10.1007/978-1-4613-9655-0
[24] Vieira H. Jr., Communications in Statistics–Simulation and Computation 39 (5) pp 971– (2010) · Zbl 05763933 · doi:10.1080/03610911003693037
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