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A Reduction Paradigm for Multivariate Laws

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  • F. Chiaromonte

Abstract

A \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.

Suggested Citation

  • F. Chiaromonte, 1997. "A Reduction Paradigm for Multivariate Laws," Working Papers ir97015, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:ir97015
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    References listed on IDEAS

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    1. Eaton, M. L. & Tyler, D., 1994. "The Asymptotic Distribution of Singular-Values with Applications to Canonical Correlations and Correspondence Analysis," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 238-264, August.
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    Cited by:

    1. Francesca Chiaromonte & R. Cook, 2002. "Sufficient Dimension Reduction and Graphics in Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(4), pages 768-795, December.
    2. F. Chiaromonte, 1998. "On Multivariate Structures and Exhaustive Reductions," Working Papers ir98080, International Institute for Applied Systems Analysis.

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