The Annals of Mathematical Statistics

Tests of Composite Hypotheses for the Multivariate Exponential Family

T. K. Matthes and D. R. Truax

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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


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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.