On Multivariate Structures and Exhaustive Reductions

F. Chiaromonte

Working Papers from International Institute for Applied Systems Analysis

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.

Date: 1998-11
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