Summary
The object of the paper is to find directions along which multivariate observations have the greatest multivariate skewness or kurtosis in an appropriate sense. Typical measures of multivariate skewness and kurtosis are Malkovich and Afifi’s (1973) b1 * and b2 *, which are essentially nonlinear maximization problems. To avoid this nonlinearity we present an approach to reduce the above problems to easier ones, which are eigenvalue problems in linear algebra and closely related to some types of measures of multivariate skewness and kurtosis. By using the resultant directions we can project observations into the sample space and check normality of the data through probability plots and scatter plots. We also show that the proposed approach enables us to extend the usual principal component analysis to a higher order case.
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References
Isogai, T. (1983). On measures of multivariate skewness and kurtosis. Mathematica Japonica 28, 251–261.
Isogai, T. (1985) Note on statistics from the 3rd and 4th order multivariate cumulants. Studies in Humanities and Social Sciences 33. Osaka Univ., 67–72.
Malkovich, J.F. and Afifi, A.A. (1973). On tests for multivariate normality. J.Am.Statist.Assoc., 68, 176–179.
Mardia, K.V. (1970). Measures of multivariate skewness and kurtosis. Biometrika 57, 519–530.
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© 1988 Physica-Verlag Heidelberg
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Isogai, T. (1988). Data Plotting Methods for Checking Multivariate Normality and Related Ideas. In: Edwards, D., Raun, N.E. (eds) Compstat. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46900-8_10
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DOI: https://doi.org/10.1007/978-3-642-46900-8_10
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0411-9
Online ISBN: 978-3-642-46900-8
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