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 -