## The Annals of Mathematical Statistics

### Two-Sample Procedures in Simultaneous Estimation

W. C. Healy, Jr

#### 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

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