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On Multivariate Structures and Exhaustive Reductions

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  • F. Chiaromonte

Abstract

Simplified representations of multivariate laws, and in particular those allowing one to decrease the dimension while preserving structural information, are of paramount importance in statistical analysis. This paper concerns the \f2theoretical premises\f1 of simplification. We introduce a framework that allows us to specify as \f2partitions\f1 of probability laws on a Euclidian space, we show how they can be generated via \f2partial orders\f1, or \f2binary operation\f1 and \f2noise classes\f1. Moreover, the framework allows us to identify \f2simplified representations\f1 that are guaranteed to be \f2exhaustive\f1 with respect to such definitions, and might live in \f2lower dimensions\1.

Suggested Citation

  • F. Chiaromonte, 1998. "On Multivariate Structures and Exhaustive Reductions," Working Papers ir98080, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:ir98080
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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.
    2. F. Chiaromonte, 1997. "A Reduction Paradigm for Multivariate Laws," Working Papers ir97015, International Institute for Applied Systems Analysis.
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