The Annals of Statistics

Exact Bahadur Efficiencies for Tests of the Multivariate Linear Hypothesis

H. K. Hsieh

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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

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

First available in Project Euclid: 12 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F20
Secondary: 62H15: Hypothesis testing 62F05: Asymptotic properties of tests

Multivariate linear hypothesis exact slopes exact Bahadur efficiency asymptotically optimal sequence


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.

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