Multivariate skewness and kurtosis measures

Multivariate skewness and kurtosis measures

Classical measures of skewness and kurtosis for a random vector were introduced by Mardia in 1970 as scalars. We define the skewness measure  as a p-vector while the kurtosis is characterized by a p x p -matrix. The introduced notions are extensions of corresponding measures of Mardia (1970) and Mòri, Rohatgi & SŸekely (1993). Basic properties of the characteristics are examined and compared with results literature. Expressions of the measures of skewness and kurtosis are derived for the multivariate Laplace distribution. The kurtosis matrix is used in Independent Component Analysis (ICA) where  solution of an eigenvalue problem of the kurtosis matrix  determines the transformation matrix of interest.

Lisätietoja: Kimmo Ivori, etunimi.sukunimi@uta.fi