Multivariate skewness and kurtosis measures with an application in ICA
Journal of Multivariate Analysis
Symmetric Tensors and Symmetric Tensor Rank
SIAM Journal on Matrix Analysis and Applications
Tensor Decompositions and Applications
SIAM Review
Supervised learning of multivariate skew normal mixture models with missing information
Computational Statistics
Eigenvectors of a kurtosis matrix as interesting directions to reveal cluster structure
Journal of Multivariate Analysis
Principal points of a multivariate mixture distribution
Journal of Multivariate Analysis
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The paper shows that the fourth cumulant of a finite mixture distribution might be decomposed into the mean of the components' fourth cumulants and the fourth cumulant of the components' means, when the mixture's components have the same second and third cumulants. Statistical applications include robustness properties of likelihood-based testing procedures and kurtosis-based projection methods. Practical relevance of theoretical results in the paper are illustrated with two well-known data sets.