## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 27, Number 3 (1956), 616-623.

### The Admissibility of Hotelling's $T^2$-Test

#### Abstract

In Section 3 we shall prove a theorem based on a method of A. Birnbaum [1] and E. Lehmann concerning the admissibility of certain tests of simple hypotheses in multivariate exponential families. In Section 4 we compute the supporting hyperplanes of the convex acceptance region in some of the most common applications of Hotelling's $T^2$-test and show that the theorem of Section 3 implies the admissibility of this test. In Section 5 we point out some of the limitations of the method of this paper.

#### Article information

**Source**

Ann. Math. Statist., Volume 27, Number 3 (1956), 616-623.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177728171

**Digital Object Identifier**

doi:10.1214/aoms/1177728171

**Mathematical Reviews number (MathSciNet)**

MR80413

**Zentralblatt MATH identifier**

0073.14301

**JSTOR**

links.jstor.org

#### Citation

Stein, Charles. The Admissibility of Hotelling's $T^2$-Test. Ann. Math. Statist. 27 (1956), no. 3, 616--623. doi:10.1214/aoms/1177728171. https://projecteuclid.org/euclid.aoms/1177728171