A Bonferroni selection procedure when using commom random numbers with unknown variances

ABSTRACT

This paper presents a Bonferroni procedure for selecting the alternative with the largest mean when the variances are unknown and unequal and correlation is induced among the observations for each alternative by common random numbers. Simulation results show that the Bonferroni procedure is more efficient than Dudewicz and Dalal's procedure when the percentage of variance reduction is high.

REFERENCES

• 1: Dudewicz, E. J. 1971, "Nonexistence of a Single-Sample Selection Procedure Whose P(CS) is independent of the Variances," South African Statistical Journal, Vol 4-6, pp. 37 -39.
• 2: Dudewicz, E. J. and Dalal, S. R. 1975, "Allocation of Observations in Ranking and Selection with Unequal Variances," Sankhya, Vol. 37, pp.28-78.
• 3: Kleijnen, J. P. C. 1974, Statistical Techniques in Simulation, Part i, Ma-rcel-Dekker, New York.
• 4: Lehman, E. L. 1959, Testing Statistical Hypotheses, John Wiley, New York, p.203.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

Additional Classification:
  G. Mathematics of Computing

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING

General Terms:
Design, Performance, Theory

Keywords:
Bonferroni inequality, common random numbers, selection, variance reduction