The Annals of Mathematical Statistics

Two-Sample Procedures in Simultaneous Estimation

W. C. Healy, Jr

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728176

Digital Object Identifier
doi:10.1214/aoms/1177728176

Mathematical Reviews number (MathSciNet)
MR81041

Zentralblatt MATH identifier
0075.14603

JSTOR
links.jstor.org

Citation

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


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