A Reduction Paradigm for Multivariate Laws
AbstractA \f2reduction paradigm\f1 is a theoretical framework which provides a definition of structures for multivariate laws, and allows to simplify their representation and statistical analysis. The main idea is to decompose a law as the superimposition of a \f2structural term\f1 and a \f2noise\f1, so that the latter can be neglected \f2without loss of information on the structure\f1. When the lower structural term is supported by a lower-dimensional affine subspace, an \f2exhaustive dimension reduction\f1 is achieved. We describe the reduction paradigm that results from selecting white noises, and convolution as superposition mechanism.
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Bibliographic InfoPaper provided by International Institute for Applied Systems Analysis in its series Working Papers with number ir97015.
Date of creation: Mar 1997
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- F. Chiaromonte, 1998. "On Multivariate Structures and Exhaustive Reductions," Working Papers ir98080, International Institute for Applied Systems Analysis.
- Francesca Chiaromonte & R. Cook, 2002. "Sufficient Dimension Reduction and Graphics in Regression," Annals of the Institute of Statistical Mathematics, Springer, vol. 54(4), pages 768-795, December.
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