A new test for multivariate normality

Journal of Multivariate Analysis

Volumn 93, Issue 1, 2005, Pages 58-80

  Székely, Gábor J ^a   Rizzo, Maria L ^b  

^a BOWLING GREEN STATE UNIVERSITY   (United States)

^b OHIO UNIVERSITY   (United States)

Author keywords

BHEP test; Goodness of fit; Henze Zirkler test; Multivariate kurtosis; Multivariate skewness; Projection pursuit; Strictly negative definite

Indexed keywords

EID: 7044235251     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmva.2003.12.002     Document Type: Article

References (29)

1. Anderson T. Darling D. A test of goodness-of-fit J. Amer. Statist. Assoc. 49 1954 765-769
2. Baringhaus L. Henze N. A consistent test for multivariate normality based on the empirical characteristic function Metrika 35 1988 339-348
3. Baringhaus L. Henze N. Limit distributions for Mardia's measure of multivariate skewness Ann. Statist. 20 1992 1889-1902
4. Bickel P.J. Götze F. van Zwet W.R. The Edgeworth expansion for U-statistics of degree two Ann. Statist. 14 4 1986 1463-1484
5. Bowman A.W. Foster P.J. Adaptive smoothing and density based tests of multivariate normality J. Amer. Statist. Assoc. 88 1993 529-537
6. Cui H. Cheng P. The P-values of testing for multinormality based on the PP skewness and kurtosis Progr. Nat. Sci. 6 3 1996 277-283
7. Epps T.W. Pulley L.B. A test for normality based on the empirical characteristic function Biometrika 70 1983 723-726
8. Fang K.-T. Wang Y. Number Theoretic Methods in Statistics 1994 Chapman & Hall New York
9. Götze F. Asymptotic expansions for bivariate von Mises functionals Z. Wahrsch. Verw. Gebiete 50 1979 333-355
10. Henze N. On Mardia's kurtosis test for multivariate normality Comm. Statist. Theory Methods 23 1994 1031-1045
11. Henze N. Wagner T. A new approach to the BHEP tests for multivariate normality J. Multivariate Anal. 62 1997 1-23
12. Henze N. Zirkler B. A class of invariant and consistent tests for multivariate normality Comm. Statist. Theory Methods 19 1990 3595-3617
13. Hoeffding W. A class of statistics with asymptotically normal distribution Ann. Math. Statist. 49 1948 293-325
14. Horswell R.L. Looney S.W. A comparison of tests for multivariate normality that are based on measures of multivariate skewness and kurtosis J. Statist. Comput. Simul. 42 1992 21-38
15. Malkovich J.F. Afifi A.A. On tests for multivariate normality J. Amer. Statist. Assoc. 68 1973 519-530
16. Mardia K.V. Measures of multivariate skewness and kurtosis with applications Biometrika 57 1970 519-530
17. d Discrete Math. 226 2001 347-349
18. Nikitin Y. Asymptotic Efficiency of Nonparametric Tests 1995 Cambridge University Press New York
19. Romeu J.L. Ozturk A. A comparative study of goodness-of-fit tests for multivariate normality J. Multivariate Anal. 46 1993 309-334
20. Santaló L.A. Integral Geometry and Geometric Probability 1976 Addison-Wesley Reading, MA
21. Serfling R.J. Approximation Theorems of Mathematical Statistics 1980 Wiley New York
22. Solomon H. Geometric Probability 1978 Society for Industrial and Applied Mathematics Philadelphia, PA
23. Székely G.J. Contests in Higher Mathematics 1996 Springer New York
24. Székely G.J. Pre-limit and post-limit theorems for statistics In: Rao C.R. Székely G.J. (Eds.) Statistics for the 21st Century 2001 411-422 Marcel Dekker New York
25. Székely G.J. Móri T.F. A characteristic measure of asymmetry and its application for testing diagonal symmetry Comm. Statist. Theory Methods 30 8&9 2001 1633-1639
26. Thas O. Ottoy J.P. Some generalizations of the Anderson-Darling statistic Statist. Probab. Lett. 64 2003 255-261
27. van der Vaart A.W. Asymptotic Statistics 1998 Cambridge University Press New York
28. Zhu L.-X. Fang K.-T. Bhatti M.I. On estimated projection pursuit-type Cramer-von Mises Statistics J. Multivariate Anal. 63 1997 1-14
29. Zhu L.-X. Wong H.L. Fang K.-T. A test for multivariate normality based on sample entropy and projection pursuit J. Statist. Plann. Inference 45 1995 373-385