Multivariate tests based on left-spherically distributed linear scores

In this paper, a method for multivariate testing based on low-dimensional, data-dependent, linear scores is proposed. The new approach reduces the dim ensionality of observations and increases the stability of the solutions. T he method is reliable, even if there are many redundant variables. As a key feature, the score coefficients are chosen such that a left-spherical dist ribution of the scores is reached under the null hypothesis. Therefore, wel l-known tests become applicable in high-dimensional situations, too. The pr esented strategy is an alternative to least squares and maximum Likelihood approaches. In a natural way, standard problems of multivariate analysis th us induce the occurrence of left-spherical, nonnormal distributions. Hence, new fields of application are opened up to the generalized multivariate an alysis. The proposed methodology is not restricted to normally distributed data, but can also be extended to any left-spherically distributed observat ions.