A Reduction Paradigm for Multivariate Laws
Abstract
A "reduction paradigm" 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 "structural term" and a "noise," so that the latter can be neglected "without loss of information on the structure." When the lower structural term is supported by a lower-dimensional affine subspace, an "exhaustive dimension reduction" is achieved. We describe the reduction paradigm that results from selecting white noises, and convolution as superposition mechanism.