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Skewness and kurtosis projection pursuit for the multivariate extended skew-normal and skew-Student distributions

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  • Adcock, C.J.

Abstract

This paper reports the results of a study into projection pursuit for the multivariate extended skew-normal and skew-Student distributions. Computation of the projection pursuit vectors is done using an algorithm that exploits the structure of the moments. Detailed results are reported for a range of values of the shape vector, the extension parameter and degrees of freedom. The required scale matrix and shape vectors are based on data reported in a study of diabetes. The same parameters and data are used to illustrate the role that projection pursuit can play in variable selection for regression. The differences between third and fourth order projection pursuit are not great, this being a consequence of the structure of the moments induced by the form of the distribution. There are differences depending on the choice of parameterization. Use of the central parameterization changes the structure of both the covariance matrix and the shape vector.

Suggested Citation

  • Adcock, C.J., 2026. "Skewness and kurtosis projection pursuit for the multivariate extended skew-normal and skew-Student distributions," Journal of Multivariate Analysis, Elsevier, vol. 211(C).
    • Handle: RePEc:eee:jmvana:v:211:y:2026:i:c:s0047259x25001289
    DOI: 10.1016/j.jmva.2025.105533
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    References listed on IDEAS

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