## The Annals of Statistics

- Ann. Statist.
- Volume 7, Number 6 (1979), 1231-1245.

### Exact Bahadur Efficiencies for Tests of the Multivariate Linear Hypothesis

#### Abstract

The notion of Bahadur efficiency is used to compare multivariate linear hypothesis tests based on six criteria: (1) Roy's largest root, (2) the likelihood ratio test, (3) the Lawley-Hotelling trace, (4) Pillai's trace, (5) Wilks' $U$, and (6) Olson's statistic. Bahadur exact slope is computed for each statistic as a function of noncentrality parameters using results for probabilities of large deviations. The likelihood ratio test is shown to be asymptotically optimal in the sense that its slope attains the optimal information value, and the remaining tests are shown not to be asymptotically optimal. Inequalities are derived for the slopes showing order of preference.

#### Article information

**Source**

Ann. Statist., Volume 7, Number 6 (1979), 1231-1245.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176344842

**Digital Object Identifier**

doi:10.1214/aos/1176344842

**Mathematical Reviews number (MathSciNet)**

MR550146

**Zentralblatt MATH identifier**

0453.62042

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F20

Secondary: 62H15: Hypothesis testing 62F05: Asymptotic properties of tests

**Keywords**

Multivariate linear hypothesis exact slopes exact Bahadur efficiency asymptotically optimal sequence

#### Citation

Hsieh, H. K. Exact Bahadur Efficiencies for Tests of the Multivariate Linear Hypothesis. Ann. Statist. 7 (1979), no. 6, 1231--1245. doi:10.1214/aos/1176344842. https://projecteuclid.org/euclid.aos/1176344842