Tests for multivariate normality -- a critical review with emphasis on weighted L2L^2-statistics

This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted $L^2$-statistics. Since weighted $L^2$-statistics typically have limit normal distributions under fixed alternatives to normality, they open ground for a neighborhood of model validation for normality. The paper also reviews several other invariant tests for this problem, notably the energy test, and it presents the results of a large-scale simulation study. All tests under study are implemented in the accompanying R-package mnt

Tests for multivariate normality—a critical review with emphasis on weighted L2L^2-statistics

This article gives a synopsis on new developments in affine invariant tests for multivariate normality in an i.i.d.-setting, with special emphasis on asymptotic properties of several classes of weighted L$^{2}$-statistics. Since weighted L$^{2}$-statistics typically have limit normal distributions under fixed alternatives to normality, they open ground for a neighborhood of model validation for normality. The paper also reviews several other invariant tests for this problem, notably the energy test, and it presents the results of a large-scale simulation study. All tests under study are implemented in the accompanying R-package mnt

Projection pursuit methods for exploratory supervised classification

In high-dimensional data, one often seeks a few interesting low-dimensional projections which reveal important aspects of the data. Projection pursuit is a procedure for searching high-dimensional data for interesting low-dimensional projections via the optimization of a criterion function called the projection pursuit index. Very few projection pursuit indices incorporate class or group information in the calculation, and hence can be adequately applied to supervised classification problems. We introduce new indices derived from linear discriminant analysis that can be used for exploratory supervised classification.;When we have the small number of observations relative to the number of variables, the class structure of optimal projection can be biased too much. In this situation, most of classical multivariate analysis methods also be problematic, too. We discuss how the sample size and dimensionality are related, and we propose a new projection pursuit index that considers the penalty for the projection coefficients and overcomes the small number of observation problem

Dimension-reduction and discrimination of neuronal multi-channel signals

Dimensionsreduktion und Trennung neuronaler Multikanal-Signale