Seminar Multivariate Skewness: a Tensor Approach

Abstract
The skewness of a random variable is often measured by its third standardized moment. Its multivariate generalization is the third standardized moment matrix, which conveniently arranges all the third-order moments of a standardized random vector. It might be regarded as the matrix version of a symmetric, third-order tensor. The best-known measures of multivariate skewness are simple functions of the third standardized moment matrix and have a straightforward tensor interpretation. This talk highlights the connections between skewness measures and tensor concepts, as for example tensor rank, tensor eigenvector and tensor contraction. The related statistical applications include multivariate normality testing, independent component analysis, model-based clustering, projection pursuit, density estimation, financial econometrics and spatial statistics.

Organizzatore
Christian Hennig