97-06
Multivariate Tests Based on Left-Spherically Distributed Linear Scores
by Läuter, J,; Glimm, E.; Kropf, S.
Preprint series: 97-06, 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: In this paper, a method for multivariate testing based on low-dimensional, data-dependent, linear scores is proposed. The new approach reduces the dimensionalityof 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 coefficientscan be chosen such that a left-spherical distribution of the scores is reached under thenull hypothesis. Therefore, well-known tests become applicable in high-dimensionalsituations, 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, butcan also be extended to any left-spherically distributed observations.
Keywords: Multivariate test, linear scores, spherical distribution, generalized multivariateanalysis, exact test, null robustness.