## The Annals of Statistics

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

H. K. Hsieh

#### 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