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

Research output: Contribution to journal › Article › peer-review

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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title = "The canonical decomposition of bivariate distributions",

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 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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N2 - 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.

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.

KW - Bivariate distribution

KW - Canonical correlation

KW - Spectral theorem

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UR - https://www.scopus.com/pages/publications/0041074924#tab=citedBy

U2 - 10.1016/0047-259X(76)90003-8

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

M3 - Article

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EP - 537

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 4

ER -

The canonical decomposition of bivariate distributions

Abstract

Keywords

ASJC Scopus subject areas

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