Title: The canonical kurtosis matrix
Authors: Nicola Loperfido - University of Urbino (Italy) [presenting]
Abstract: The canonical kurtosis matrix of a $p$-dimensional random vector with finite fourth moments and positive definite covariance matrix is a $p\times p$ symmetric, positive definite matrix which conveniently summarizes the fourth standardized moments of the random vector itself. The applications of the canonical kurtosis matrix include cluster analysis, outlier detection, invariant coordinate selection, independent component analysis and projection pursuit. The main properties of the canonical kurtosis matrix are reviewed, and new ones are investigated, with special emphasis on sign-symmetry, skew-symmetry and exchangeability. The statistical applications of the canonical kurtosis matrix are illustrated with both real and simulated datasets.