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Selecting from Normal Populations the One with the Largest Absolute Mean: Common Unknown Variance Case

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Advances in Stochastic Simulation Methods

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

Rizvi (1971) studied a single-stage procedure for selecting from several normal populations the one with the largest absolute mean using the indifference-zone formulation of Bechhofer (1954), assuming that the populations have a common known variance. When the common variance is unknown, a single-stage procedure that guarantees a minimum probability of a correct selection does not exist. In this paper, a non-eliminating two-stage procedure is proposed and studied for this situation.

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References

  1. Bechhofer, R. E. (1954). A single-sample multiple decision procedure for ranking means of normal populations with known variances, Annals of Mathematics and Statistics, 25 16–39.

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  5. Tamhane, A.C. and Bechhofer, R. E. (1977). A two-stage minimax procedure with screening for selecting the largest normal mean, Communications In Statistics—Theory and Methods, A6 1003–1033.

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  6. Tamhane, A. C. and Bechhofer, R. E. (1979). A two-stage minimax procedure with screening for selecting the largest normal mean (II): An improved PCS lower bound and associated tables Communications In Statistics—Theory and Methods, A8 337–358.

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Jeyaratnam, S., Panchapakesan, S. (2000). Selecting from Normal Populations the One with the Largest Absolute Mean: Common Unknown Variance Case. In: Balakrishnan, N., Melas, V.B., Ermakov, S. (eds) Advances in Stochastic Simulation Methods. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1318-5_16

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  • DOI: https://doi.org/10.1007/978-1-4612-1318-5_16

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7091-1

  • Online ISBN: 978-1-4612-1318-5

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