论文信息 - A comparison of the performances of procedures for selecting the normal population having the largest mean when the populations have a common unknown variance

A comparison of the performances of procedures for selecting the normal population having the largest mean when the populations have a common unknown variance

We study the performances of the two-stage non-eliminating procedure of Bechhofer, Dunnett and Sobel (1954), the two-stage eliminating procedure of Gupta and Kim (1984) and the multi-stage eliminating procedure of Paulson (1964) as modified by Hartmann (1990) for selecting the normal population which has the largest mean when the common variance is unknown. Constants to implement the procedures are provided. All of these procedures are open and guarantee the indifference-zone probability require-ment of Bechhofer (1954). The following performance characteristics are estimated by Monte Carlo sampling: the achieved probability of a correct selection, the expected number of vector-observations and the expected total number of observations to termination of experimentation. The critical role of the common initial sample size per population is discussed. Guidance is provided as to which procedure to use in different environments.

M. Hartmann | C. Dunnett | R. Bechhofer | D. Goldsman

[1] R. Bechhofer. A Single-Sample Multiple Decision Procedure for Ranking Means of Normal Populations with known Variances , 1954 .

[2] C. Dunnett,et al. A TOW-SAMPLE MULTIPLE DECISION PROCEDURE FOR RANKING MEANS OF NORMAL POPULATIONS WITH A COMMON UNKNOWN VARIANCE , 1954 .

[3] E. Paulson. A Sequential Procedure for Selecting the Population with the Largest Mean from $k$ Normal Populations , 1964 .

[4] A. Tamhane,et al. A two-stage minimax procedure with screening for selecting the largest normal mean (ii): an improved , 1977 .

[5] S. C. Kao,et al. Sequential selectiok procedures based on confidence sequences for normal populations , 1980 .

[6] S. Gupta,et al. A Two-Stage Elimination Type Procedure for Selecting the Largest of Several Normal Means with a Common Unknown Variance. , 1982 .

[7] Shanti S. Gupta,et al. On the distribution of the studentized maximum of equally correlated normal random variables , 1985 .

[8] R. Bechhofer,et al. Percentage Points of Multivariate Student t Distributions , 1986 .

[9] M. Hartmann. An improvement on paulson s sequential ranking procedure , 1988 .

[10] David Goldsman,et al. A Comparison of the Performances of Procedures for Selecting the Normal Population Having the Largest Mean when the Variances are Known and Equal , 1989 .