The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 27, Number 3 (1956), 687-702.
Two-Sample Procedures in Simultaneous Estimation
In this paper, two-sample procedures of the type originated by Stein  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 , Scheffe  and Bose and Roy . 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.
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. https://projecteuclid.org/euclid.aoms/1177728176