Browse > Article
http://dx.doi.org/10.5351/KJAS.2004.17.3.507

Remarks on the Use of Multivariate Skewness and Kurtosis for Testing Multivariate Normality  

김남현 (홍익대학교 기초과학과)
Publication Information
The Korean Journal of Applied Statistics / v.17, no.3, 2004 , pp. 507-518 More about this Journal
Abstract
Malkovich & Afifi (1973) generalized the univariate skewness and kurtosis to test a hypothesis of multivariate normality by use of the union-intersection principle. However these statistics are hard to compute for high dimensions. We propose the approximate statistics to them, which are practical for a high dimensional data set. We also compare the proposed statistics to Mardia(1970)'s multivariate skewness and kurtosis by a Monte Carlo study.
Keywords
Multivariate normality; Skewness; Kurtosis;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Zhu, L. X., Wong, H. L. and Fang, K. T. (1995). A test for multivariate normality based on sample entropy and projection pursuit. Journal of Statistical Planning and Inference, 45, 373-385   DOI   ScienceOn
2 Henze, N. (2002). Invariant tests for multivariate normality : A critical review. Statistical Papers, 43, 467-506   DOI   ScienceOn
3 Henze, N. and Wagner, T. (1997). A new approach to the BHEP tests for multivariate normality. Journal of Multivariate Analysis, 62, 1-23   DOI   ScienceOn
4 Henze, N. and Zirkler, II. (1990). A class of invariant and consistent tests for multivariate normality. Communications in Statistics - Theory and Methods, 19, 3595-3617   DOI   ScienceOn
5 Horswell, R. L. and 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   DOI
6 Kim, N. and Bickel, P. J. (2003). The limit distribution of a test statistic for bivariate normality. Statistica Sinica, 13, 327-349   ScienceOn
7 Koziol, J. A. (1983). On assessing multivariate normality. Journal of the Royal Statistical Society, Series B, 45, 358-361
8 Machado, S. G. (1983). Two statistics for testing for multivariate normality. Biometrika, 70, 713-718   DOI   ScienceOn
9 Malkovich, J. F. and Afifi, A. A. (1973). On tests for multivariate normality. Journal of the American Statistical Association, 68, 176-179   DOI   ScienceOn
10 Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530   DOI   ScienceOn
11 Mardia, K. V. (1974). Applications of some measures of multivariate skewness and kurtosis for testing normality and robustness studies. Sankhya A, 36, 115-128
12 김남현 (2004). 다변량 정규성검정을 위한 근사 Shapiro-Wilk 통계량의 일반화. <응용통계연구>, 17, 35-47
13 Baringhaus, L. and Henze, N. (1988). A consistent test for multivariate normality based on the empirical characteristic function. Metrika, 35, 339-348   DOI
14 Baringhaus, L. and Henze, N. (1991). Limit distributions for measures of multivariate skewness and kurtosis based on projections. Journal of Multivariate Analysis, 38, 51-69   DOI
15 Baringhaus, L. and Henze, N. (1992). Limit distributions for Mardia's measure of multivariate skewness. The Annals of Statistics, 20, 1889-1902   DOI   ScienceOn
16 D'Agostino, R. B. and Stephens, M. A. (1986). Goodness-of-fit Techniques. Marcel Dekker, New York
17 de Wet, T., Venter, J. H. and van Wyk, J. W. J. (1979). The null distributions of some test criteria of multivariate normality. South African Statistical Journal, 13, 153-176
18 Fang, K. T. and Wang, Y. (1993). Number-theoretic methods in statistics. Monographs on statistics and applied probability. Chapman and Hall, London
19 Fattorini, L. (1986). Remarks on the use of the Shapiro-Wilk statistic for testing multivariate normality. Statistica, 46, 209-217
20 Mardia, K. V. (1975). Assessment of multinormality and the robustness of Hotelling's $T^2$ test. Applied Statistics, 24, 163-171   DOI   ScienceOn
21 Mardia, K. V. (1980). Tests of univariate and multivariate normality. In Handbook in Statistics (Ed. P. R. Krishnaiah), 279-320. Amsterdam, North-Holland
22 Pearson, E. S., D'Agostino, R. B. and Bowman, K. O. (1977). Tests for departure from normality: Comparison of powers. Biometrika, 64, 231-246   DOI   ScienceOn
23 Romeu, J. L. and Ozturk, A. (1993). A comparative study of goodness-of-fit tests for multivariate normality. Journal of Multivariate Analysis, 46, 309-334   DOI   ScienceOn
24 Roy, S. N. (1953). On a heuristic method of test coustruction and its use in multivariate analysis. Annals of Mathematical Statistics, 24, 220-238   DOI   ScienceOn
25 Shapiro, S. S. and Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52, 591-611   DOI   ScienceOn
26 Thode, H. C. Jr. (2002). Testing for Normality. Marcel Dekker, New York
27 Zhu, L., Fang, K. T. and Bhatti, M. I. (1997). On estimated projection pursuit Cram$\`e$r-von Mises statistics. Journal of Multivariate Analysis, 63, 1-14   DOI   ScienceOn