The aim of this doctoral thesis was to investigate further properties and applications of the recently introduced two scatter matrices transformation of Oja, Sirkiä and Eriksson (2006) and Tyler, Critchley, Dümbgen and Oja (2008). We consider this transformation in the framework of multivariate model selection, robust independent component analysis and multivariate nonparametric location tests.

Especially the last one leads to robust affine invariant location tests which are highly efficient for appropriately chosen score functions. The transformation was implemented in R with a large choice for scatter functionals and made publicly available. Together with the other R packages resulting from this work, all methods discussed can be easily applied. For a practical demonstration a hemodynamic data set is analyzed using the methods discussed here.