by Läuter, J,, Glimm, E., Kropf, S..

**Series:** 1997-06, Preprints

- MSC:
- 62F35 Robustness and adaptive procedures
- 62H15 Hypothesis testing
- 62H20 Measures of association (correlation, canonical correlation, etc.)
- 62H25 Factor analysis and principal components; correspondence analysis
- 62J10 Analysis of variance and covariance
- 62J15 Paired and multiple comparisons

**Abstract:**

this paper, a method for multivariate testing based on low-dimensional, data-

dependent, linear scores is proposed. The new approach reduces the dimensionality

of observations and increases the stability of the solutions. The method is reliable,

even if there are many redundant variables. As a key feature, the score coefficients

can be chosen such that a left-spherical distribution of the scores is reached under the

null hypothesis. Therefore, well-known tests become applicable in high-dimensional

situations, too. The presented strategy is an alternative to least squares and max-

imum likelihood approaches. In a natural way, standard problems of multivari-

ate analysis thus induce the occurrence of left-spherical, non-normal distributions.

Hence, new fields of application are opened up to the generalized multivariate anal-

ysis. The proposed methodology is not restricted to normally distributed data, but

can also be extended to any left-spherically distributed observations.

**Keywords:**

Multivariate test, linear scores, spherical distribution, generalized multivariateanalysis, exact test, null robustness.