Abstract
This paper deals with the problem of selecting the population associated with the largest unknown mean from several normal populations having a common unknown coefficient of variation. Both subset selection and indifference zone approaches are studied. Based on the observed sample means and sample standard deviations, a subset selection rule is proposed. Some properties related to this selection rule are discussed. For the indifference zone approach, a two-stage elimination type selection rule is considered. If the experimenter has some prior knowledge about an upper bound on the unknown means, a modification is introduced to reduce the size of the selected subset at the first stage and also to reduce the sample size at the second stage. An example is provided which indicates that the saving in the total sample size is quite significant if this prior knowledge is taken into consideration in designing the selection rule. It is shown how to implement the above selection rules by using several existing tables.
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References
Amemiya, T. (1973). ‘Regression analysis when the variance of the dependent variable is proportional to the square of its expectation’. J. Amer. Statist. Assoc. 68, 928–934.
Bechhofer, R. E. (1954). ‘A single sample multiple decision procedure for ranking means of normal populations with known variances’, Ann. Math. Statist. 25, 16–39.
Bechhofer, R. E., Dunnett, C. W. and Sobel, M. (1954).‘A two-sample multiple decision procedure for ranking means of normal populations with a common unknown variance’, Biometrika 41, 170–176.
Dudewicz, E. J. and Dalai, S. R. (1975). ‘Allocation of observations in ranking and selection with unequal variances’, Sankhya B37, 28–78.
Gleser, L. J. and Healy, J. D. (1976). ‘Estimating the mean of a normal distribution with known coefficient of variation’, J. Amer. Statist. Assoc. 71, 977–981.
Gupta, S. S. (1956). ‘On a decision rule for a problem in ranking means’, Institute of Statistics Mimeo. Ser. No. 150, University of North Carolina, Chapel Hill, N.C.
Gupta, S. S. (1963). ‘Probability integrals of multivariate normal and multivariate t’,Ann. Math. Statist. 34, 792–828.
Gupta, S. S. (1965). ‘On some multiple decision (selection and ranking) rules’, Technometrics 7, 225–245.
Gupta, S. S. and Kim, W. C. (1984). ‘A two-stage elimination type procedure for selecting the largest of several normal means with a common unknown variance’, Design of Experiments: Ranking and Selection, (Eds. T. J. Santner and A. C. Tamhane), Marcel Dekker, New York, 77–94.
Gupta, S. S. and Panchapakesan, S. (1979). Multiple Decision Procedures: Methodology of Selection and Ranking Populations, John Wiley, New York.
Gupta, S. S., Panchapakesan, S. and Sohn, J. K. (1985). ‘On the distribution of the studentized maximum of equally correlated normal random variables’, Commun. Statist.-Simula. Computa. 14 (1), 103–135.
Gupta, S. S. and Singh, A. K. (1983). ‘On subset selection procedures for the largest mean from normal populations having a common known coefficient of variation’, Technical Report #83–6, Department of Statistics, Purdue University, West Lafayette, Indiana.
Gupta, S. S. and Sobel, M. (1957). ‘On a statistic which arises in selection and ranking problem’, Ann. Math. Statist. 28, 957–967.
Gupta, S. S. and Wong, W. Y. (1982). ‘Subset selection procedures for the means of normal populations with unequal variances: unequal sample sizes case’, Selecta Statistica Canadiana Vol. VI, 109–149.
Mukhopadhyay, N. (1979). ‘Some comments on two-stage selection procedures’,Commun. Statist. A8, 671–683.
Rinott, Y. (1978). ‘On two-stage selection procedures and related probability inequalities’, Commun. Statist. A7, 799–811.
Tamhane, A. C. (1978). ‘Ranking and selection problems for normal populations with common known coefficient of variation’, Sankhyā B39, 344–361.
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© 1987 D. Reidel Publishing Company
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Gupta, S.S., Liang, T. (1987). Selecting the Best Unknown Mean from Normal Populations Having a Common Unknown Coefficient of Variation. In: Bauer, P., Konecny, F., Wertz, W. (eds) Mathematical Statistics and Probability Theory. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3965-3_10
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DOI: https://doi.org/10.1007/978-94-009-3965-3_10
Publisher Name: Springer, Dordrecht
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