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On Multivariate Skewness and Kurtosis
Theory of Probability and Its Applications, 1994Summary: Let \(X\) be a \(d\)-dimensional standardized random variable \(({\mathbf E}(X) = 0\), \(\text{cov}(X) = 1)\). Then for a multivariate analogue of skewness \(s = {\mathbf E}(\| X \|^ 2 X)\) and kurtosis \(k = {\mathbf E} XX^ T XX^ T - (d + 2)I\) we show that \(\| s\|^ 2 \leq \text{tr }k + 2d\). For infinitely divisible distributions, \(\| s\|^
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