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March, 1988 Most Powerful Invariant Tests for Binormality
Zbigniew Szkutnik
Ann. Statist. 16(1): 292-301 (March, 1988). DOI: 10.1214/aos/1176350706


We investigate the problem of testing multinormality against alternatives invariant with respect to the affine group of transformations $G$ and against left-bounded alternatives defined by Szkutnik. The last problem remains invariant under a suitably chosen subgroup $G^\ast$ of $G$. Using Wijsman's theorem we find general forms of the most powerful $G$- and $G^\ast$-invariant tests for multinormality which opens the way to an extension of the one-dimensional results of Uthoff to the bivariate case. We find explicit forms of tests against bivariate exponential and bivariate uniform alternatives. A Monte Carlo approximation of the power of these tests is given. This provides us with upper bounds for the power of all invariant tests for binormality against the alternatives considered. The maximum property of the tests obtained is also studied.


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Zbigniew Szkutnik. "Most Powerful Invariant Tests for Binormality." Ann. Statist. 16 (1) 292 - 301, March, 1988.


Published: March, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0677.62052
MathSciNet: MR924872
Digital Object Identifier: 10.1214/aos/1176350706

Primary: 62H15

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • March, 1988
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