The canonical decomposition of bivariate distributions

P. L. Chesson

doi:10.1016/0047-259X(76)90003-8

The canonical decomposition of bivariate distributions

P. L. Chesson

Ecology and Evolutionary Biology

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8 Scopus citations

Abstract

The ordinary notion of a bivariate distribution has a natural generalisation. For this generalisation it is shown that a bivariate distribution can be characterised by a Hilbert space H and a family M_p, 0 ≤ p ≤ 1, of subspaces of H. H specifies the marginal distributions whilst M_p is a summary of the dependence structure. This characterisation extends existing ideas on canonical correlation.

Original language	English (US)
Pages (from-to)	526-537
Number of pages	12
Journal	Journal of Multivariate Analysis
Volume	6
Issue number	4
DOIs	https://doi.org/10.1016/0047-259X(76)90003-8
State	Published - Dec 1976

Keywords

Bivariate distribution
Canonical correlation
Spectral theorem

ASJC Scopus subject areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

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10.1016/0047-259X(76)90003-8

Cite this

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AB - The ordinary notion of a bivariate distribution has a natural generalisation. For this generalisation it is shown that a bivariate distribution can be characterised by a Hilbert space H and a family Mp, 0 ≤ p ≤ 1, of subspaces of H. H specifies the marginal distributions whilst Mp is a summary of the dependence structure. This characterisation extends existing ideas on canonical correlation.

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KW - Spectral theorem

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The canonical decomposition of bivariate distributions

Abstract

Keywords

ASJC Scopus subject areas

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