## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 38, Number 3 (1967), 681-697.

### Tests of Composite Hypotheses for the Multivariate Exponential Family

#### Abstract

This paper is concerned with testing the hypothesis that the parameter in a multivariate exponential distribution lies in a linear subspace of the natural parameter space. Our main result characterizes a complete class of tests which is independent of the particular exponential distribution. This class is, in fact, complete relative to the stronger ordering among tests which compares conditional power, given a certain statistic, pointwise. The conclusion holds without any restriction on the exponential distribution. Many of the tests are admissible, but examples show that although the class is essentially the smallest class complete relative to all exponential distributions, it is not in general minimally complete. Some special cases where the class is minimally complete are discussed.

#### Article information

**Source**

Ann. Math. Statist., Volume 38, Number 3 (1967), 681-697.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177698862

**Digital Object Identifier**

doi:10.1214/aoms/1177698862

**Mathematical Reviews number (MathSciNet)**

MR208745

**Zentralblatt MATH identifier**

0152.17802

**JSTOR**

links.jstor.org

#### Citation

Matthes, T. K.; Truax, D. R. Tests of Composite Hypotheses for the Multivariate Exponential Family. Ann. Math. Statist. 38 (1967), no. 3, 681--697. doi:10.1214/aoms/1177698862. https://projecteuclid.org/euclid.aoms/1177698862

#### Corrections

- See Correction: T. K. Matthes, D. R. Truax. Correction: Correction to Tests of Composite Hypotheses for the Multivariate Exponential Family. Ann. Math. Statist., Volume 38, Number 6 (1967), 1928--1928.Project Euclid: euclid.aoms/1177698631