TY - JOUR
T1 - Multiple comparisons with the best using common random numbers for steady-state simulations
AU - Nakayama, Marvin K.
N1 - Funding Information:
The author would like to thank the referees for providing comments that improved the quality of the paper. Also, this work is supported, in part, by the National Science Foundation under Grant No. DMI-9624469 and by the New Jersey Institute of Technology under Grant No. 421180.
PY - 2000/4/1
Y1 - 2000/4/1
N2 - Suppose that there are k≥2 different systems (i.e., stochastic processes), where each system has an unknown steady-state mean performance. We consider the problem of running a single-stage simulation using common random numbers to construct simultaneous confidence intervals for μi-maxj≠iμj,i=1,2,...,k. This is known as multiple comparisons with the best (MCB). Under an assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem, we prove that our confidence intervals are asymptotically valid (as the run lengths of the simulations of each system tends to infinity). We develop algorithms for two different cases: when the asymptotic covariance matrix has sphericity, and when the covariance matrix is arbitrary.
AB - Suppose that there are k≥2 different systems (i.e., stochastic processes), where each system has an unknown steady-state mean performance. We consider the problem of running a single-stage simulation using common random numbers to construct simultaneous confidence intervals for μi-maxj≠iμj,i=1,2,...,k. This is known as multiple comparisons with the best (MCB). Under an assumption that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem, we prove that our confidence intervals are asymptotically valid (as the run lengths of the simulations of each system tends to infinity). We develop algorithms for two different cases: when the asymptotic covariance matrix has sphericity, and when the covariance matrix is arbitrary.
KW - 60F17
KW - 62J15
KW - 62M10
KW - Common random numbers
KW - Functional central limit theorem
KW - Multiple comparisons
KW - Output analysis
KW - Primary 68U20
KW - Secondary 65C05
KW - Stochastic simulation
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U2 - 10.1016/S0378-3758(99)00064-6
DO - 10.1016/S0378-3758(99)00064-6
M3 - Article
AN - SCOPUS:0008548796
SN - 0378-3758
VL - 85
SP - 37
EP - 48
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
IS - 1-2
ER -