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2012 | 49 | 2 | 159-175
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
49
Numer
2
Strony
159-175
Opis fizyczny
Daty
wydano
2012-12-01
online
2013-08-17
Twórcy
autor
  • Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-934 Lublin, Poland, zofia.hanusz@up.lublin.pl
  • Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-934 Lublin, Poland, joanna.tarasinska@up.lublin.pl
  • Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin, Akademicka 13, 20-934 Lublin, Poland, zbigniew.osypiuk@up.lublin.pl
Bibliografia
  • Henze N., Zirkler B. (1990): A class of invariant consistent tests for multivariate normality. Communication in Statistics - Theory and Methods 19: 3595-3617.
  • Henze N. (1994): On Mardia’s kurtosis test for multivariate normality. Communication in Statistics - Theory and Methods 23: 1031-1945.
  • Horswell R.L., Looney S.W. (1992): A comparison of tests for multivariate normality that are based on measures of multivariate skewness and kurtosis. Journal of Statistical Computation and Simulation 42: 21-38.[Crossref]
  • Johnson M.E. (1987): Multivariate Statistical Simulation. New York: John Wiley & Sons.
  • Layard M.W.J. (1974). A Monte Carlo comparison of tests for equality of covariance matrices. Biometrika 16: 461-465.
  • Looney S.W. (1995): How to use tests for univariate normality to assess multivariate normality. The American Statistician 29: 64-70.
  • Mardia K.V. (1970): Measures of multivariate skewness and kurtosis with applications. Biometrika 57: 519-530.[Crossref]
  • Mardia K.V. (1974): Applications of some measures of multivariate skewness and kurtosis for testing normality and robustness studies. Sankhya B 36:115-128.
  • Mardia K.V. (1980): Tests of univariate and multivariate normality. In: Handbook of Statistics 1, ed. P.R. Krishnaiah, Amsterdam: North-Holland Publishing Company: 279-320.
  • Mardia K.V., Kanazawa M. (1983): The null distribution of multivariate kurtosis. Communication in Statistics - Simulation and Computation 12: 569-576.
  • Mardia K.V., Kent J.T., Bibby J.M. (1979): Multivariate Analysis. New York: Academic Press.
  • Mecklin C.J., Mundfrom D.J. (2004): An appraisal and bibliography of tests for multivariate normality. International Statistical Review 72: 123-138.
  • 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.
  • SAS Institute Inc. (1989): SAS/IML Software: Usage and Reference, Version 6 (First Edition), SAS Institute, Cary, NC.
  • Srivastava M.S. (1984). A measure of skewness and kurtosis and a graphical method for assessing multivariate normality. Statistics & Probability Letters 2: 263-267.[Crossref]
  • Tiku M.L., Tan W.Y., Balakrishnan N. (1986): Robust Inference. New York: Marcel Dekker.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_bile-2013-0012
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