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September, 1956 Two-Sample Procedures in Simultaneous Estimation
W. C. Healy Jr
Ann. Math. Statist. 27(3): 687-702 (September, 1956). DOI: 10.1214/aoms/1177728176


In this paper, two-sample procedures of the type originated by Stein [4] are developed for a number of problems in simultaneous estimation. The results include the construction of simultaneous confidence intervals of prescribed length or lengths and confidence coefficient $1 - \alpha$ for (1) all normalized linear functions of means, (2) all differences between means, and (3) the means of $k$ independent normal populations with common unknown variance. Simultaneous confidence intervals of length $l$ and confidence coefficients known to be not less than $1 - \alpha$ are constructed for all normalized linear functions of the means of a general multivariate normal population. The single sample analogues of these problems have been discussed by Tukey [5], Scheffe [6] and Bose and Roy [7]. Also, a confidence region having prescribed diameter (or volume) and confidence coefficient $1 - \alpha$ is constructed for the mean vector in the general multivariate normal case. The procedures depend only on known and tabulated distributions. Illustrative applications from the analysis of variance are described.


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W. C. Healy Jr. "Two-Sample Procedures in Simultaneous Estimation." Ann. Math. Statist. 27 (3) 687 - 702, September, 1956.


Published: September, 1956
First available in Project Euclid: 28 April 2007

zbMATH: 0075.14603
MathSciNet: MR81041
Digital Object Identifier: 10.1214/aoms/1177728176

Rights: Copyright © 1956 Institute of Mathematical Statistics

Vol.27 • No. 3 • September, 1956
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