The Annals of Mathematical Statistics

Two-Sample Procedures in Simultaneous Estimation

W. C. Healy, Jr

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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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Ann. Math. Statist., Volume 27, Number 3 (1956), 687-702.

First available in Project Euclid: 28 April 2007

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Healy, W. C. Two-Sample Procedures in Simultaneous Estimation. Ann. Math. Statist. 27 (1956), no. 3, 687--702. doi:10.1214/aoms/1177728176.

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