## The Annals of Mathematical Statistics

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

Charles Stein

#### 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

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
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