Biometrical Letters Vol. 49(2), 2012, pp. 159-175
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ON THE SMALL SAMPLE PROPERTIES OF VARIANTS OF MARDIA'S AND SRIVASTAVA'S KURTOSIS-BASED TESTS FOR MULTIVARIATE NORMALITY
Zofia Hanusz, Joanna Tarasińska, Zbigniew Osypiuk Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-934 Lublin, Poland, e-mail: zofia.hanusz@up.lublin.pl; joanna.tarasinska@up.lublin.pl, zbigniew.osypiuk@up.lublin.pl |
The kurtosis-based tests of Mardia and Srivastava for assessing multivariate normality (MVN) are considered. The asymptotic standard normal distribution of their test statistics, under normality, is often misused for too small samples. The purpose of this paper is to suggest mean-and-variance corrected versions of the Mardia and Srivastava test statistics. Simulation studies evaluating both the true sizes and the powers of original and corrected tests against selected alternatives are presented and compared to the size and the power of the Henze–Zirkler test. The proposed corrected statistics have empirical sizes closer to a nominal significance level than the original ones. It is also shown that the corrected versions of the tests can be more powerful than the original ones.
Henze–Zirkler test, true size studies, power studies, heavy-tailed distributions, light-tailed distributions
