Abstract: In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.
Abstract: A dissimilarity measure between the empiric
characteristic functions of the subsamples associated to the different
classes in a multivariate data set is proposed. This measure can be
efficiently computed, and it depends on all the cases of each class. It
may be used to find groups of similar classes, which could be joined
for further analysis, or it could be employed to perform an
agglomerative hierarchical cluster analysis of the set of classes. The
final tree can serve to build a family of binary classification models,
offering an alternative approach to the multi-class SVM problem. We
have tested this dendrogram based SVM approach with the oneagainst-
one SVM approach over four publicly available data sets,
three of them being microarray data. Both performances have been
found equivalent, but the first solution requires a smaller number of
binary SVM models.