## The Annals of Mathematical Statistics

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

### Two-Sample Procedures in Simultaneous Estimation

#### 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