Title: Multivariate kurtosis, projection pursuit and tensor eigenvectors: A triangulation
Authors: Nicola Loperfido - University of Urbino (Italy) [presenting]
Abstract: Kurtosis-based projection pursuit looks for interesting data structures by means of projections with either maximal or minimal kurtosis. The projecting directions and the corresponding kurtoses coincide with the tensor eigenvectors and tensor eigenvalues of the fourth standardized moment, regarded as a fourth-order, real and symmetric tensor. Their properties are investigated both in the general case and for some statistical models, as for examples finite mixtures and hidden truncation models. Kurtosis-based projection pursuit is closely related to outlier detection, cluster analysis, independent component analysis, normality testing and portfolio selection. Its practical relevance is illustrated with well-known datasets: the Iris dataset, the Crab dataset and the Australian Athletes dataset.