The canonical decomposition of bivariate distributions

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)526-537
Number of pages12
JournalJournal of Multivariate Analysis
Volume6
Issue number4
DOIs
StatePublished - 1976
Externally publishedYes

Fingerprint

Canonical Decomposition
Bivariate Distribution
Hilbert spaces
Decomposition
Canonical Correlation
Dependence Structure
Marginal Distribution
Hilbert space
Subspace
Generalization
Family

Keywords

  • Bivariate distribution
  • Canonical correlation
  • Spectral theorem

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Numerical Analysis
  • Statistics and Probability

Cite this

The canonical decomposition of bivariate distributions. / Chesson, Peter.

In: Journal of Multivariate Analysis, Vol. 6, No. 4, 1976, p. 526-537.

Research output: Contribution to journalArticle

@article{de7ba1319dad4a499947a6833293181d,
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.",
keywords = "Bivariate distribution, Canonical correlation, Spectral theorem",
author = "Peter Chesson",
year = "1976",
doi = "10.1016/0047-259X(76)90003-8",
language = "English (US)",
volume = "6",
pages = "526--537",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",
number = "4",

}

TY - JOUR

T1 - The canonical decomposition of bivariate distributions

AU - Chesson, Peter

PY - 1976

Y1 - 1976

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

UR - http://www.scopus.com/inward/record.url?scp=0041074924&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041074924&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0041074924

VL - 6

SP - 526

EP - 537

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 4

ER -