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Transformations, Multivariate

Statistical Theory and Methods

  1. David Ruppert

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vam050

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Ruppert, D. 2006. Transformations, Multivariate. Encyclopedia of Environmetrics. 6.

Author Information

  1. Cornell University, NY, USA

Publication History

  1. Published Online: 15 SEP 2006


Many of the classical techniques of multivariate analysis, e.g. principal components, factor analysis, canonical correlations, and linear discriminant analysis are based upon the assumption that the data have been sampled from a multivariate normal distribution. These techniques can be quite nonrobust towards some types of deviations from normality, for example heavy-tails or skewness. When the data deviate from normality, multivariate transformation can re-express the data as a sample closer to being multivariate normal. In principle, the methodologies developed for transformation to multivariate normality could be used to transform to other multivariate distributions. However, the normal distribution plays such a central role in multivariate analysis that transformation to other multivariate targets has not been considered as important and will not be discussed in this article.