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On the central moments of linear combinations of multivariate random variables: A contribution to the determination of maximum and minimum values. (Italian. English summary) Zbl 0591.62046

Summary: In the statistical analysis of multivariate distributions, the linear combinations for which the standardized third and fourth moments have their maximum or minimum value may by utilized, for instance, to inquire on robustness, test on multinormality or identify possible outliers or clusters.
In this note some theoretical results are shown widening the concept of a matrix eigenvalue and eigenvector which are obtained by the author in determining such combinations. Explicit solutions are given for bivariate distributions, while an iterative method is suggested for those of greater dimensions.

MSC:

62H10 Multivariate distribution of statistics
15A18 Eigenvalues, singular values, and eigenvectors
62H99 Multivariate analysis
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