Multiple comparisons with the best using common random numbers for steady-state simulations

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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.

Original languageEnglish (US)
Pages (from-to)37-48
Number of pages12
JournalJournal of Statistical Planning and Inference
Issue number1-2
StatePublished - Apr 1 2000

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


  • 60F17
  • 62J15
  • 62M10
  • Common random numbers
  • Functional central limit theorem
  • Multiple comparisons
  • Output analysis
  • Primary 68U20
  • Secondary 65C05
  • Stochastic simulation


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