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June, 1986 Testing for Normality in Arbitrary Dimension
Sandor Csorgo
Ann. Statist. 14(2): 708-723 (June, 1986). DOI: 10.1214/aos/1176349948


The univariate weak convergence theorem of Murota and Takeuchi (1981) is extended for the Mahalanobis transform of the $d$-variate empirical characteristic function, $d \geq 1$. Then a maximal deviation statistic is proposed for testing the composite hypothesis of $d$-variate normality. Fernique's inequality is used in conjunction with a combination of analytic, numerical analytic, and computer techniques to derive exact upper bounds for the asymptotic percentage points of the statistic. The resulting conservative large sample test is shown to be consistent against every alternative with components having a finite variance. (If $d = 1$ it is consistent against every alternative.) Monte Carlo experiments and the performance of the test on some well-known data sets are also discussed.


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Sandor Csorgo. "Testing for Normality in Arbitrary Dimension." Ann. Statist. 14 (2) 708 - 723, June, 1986.


Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0615.62060
MathSciNet: MR840524
Digital Object Identifier: 10.1214/aos/1176349948

Primary: 62H15
Secondary: 62F03, 62F05

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 2 • June, 1986
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