# 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

Biometrical Letters (2012)

- Volume: 49, Issue: 2, page 159-175
- ISSN: 1896-3811

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topZofia Hanusz, Joanna Tarasińska, and Zbigniew Osypiuk. "On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality." Biometrical Letters 49.2 (2012): 159-175. <http://eudml.org/doc/268824>.

@article{ZofiaHanusz2012,

abstract = {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.},

author = {Zofia Hanusz, Joanna Tarasińska, Zbigniew Osypiuk},

journal = {Biometrical Letters},

keywords = {Henze-Zirkler test; true size studies; power studies; heavy-tailed distributions; light-tailed distributions; multivariate normality; graphical methods; test for multivariate normality; power; size},

language = {eng},

number = {2},

pages = {159-175},

title = {On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality},

url = {http://eudml.org/doc/268824},

volume = {49},

year = {2012},

}

TY - JOUR

AU - Zofia Hanusz

AU - Joanna Tarasińska

AU - Zbigniew Osypiuk

TI - On the small sample properties of variants of Mardia’s and Srivastava’s kurtosis-based tests for multivariate normality

JO - Biometrical Letters

PY - 2012

VL - 49

IS - 2

SP - 159

EP - 175

AB - 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.

LA - eng

KW - Henze-Zirkler test; true size studies; power studies; heavy-tailed distributions; light-tailed distributions; multivariate normality; graphical methods; test for multivariate normality; power; size

UR - http://eudml.org/doc/268824

ER -

## References

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- R Development Core Team (2008): R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
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