# Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach.

SORT (2003)

• Volume: 27, Issue: 2, page 165-174
• ISSN: 1696-2281

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## Abstract

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Asymptotic study of canonical correlation analysis gives the opportunity to present the different steps of an asymptotic study and to show the interest of an operator and tensor approach of multidimensional asymptotic statistics rather than the classical, matrix and analytic approach. Using the last approach, Anderson (1999) assumes the random vectors to have a normal distribution and the non zero canonical correlation coefficients to be distinct. The new approach we use, Fine (2000), is coordinate-free, distribution-free and permits to have no restriction on the canonical correlation coefficients multiplicity order. Of course, when vectors have a normal distribution and when the non zero canonical correlation coefficients are distinct, it is possible to find again Anderson's results but we diverge on two of them. In this methodological presentation, we insist on the analysis frame (Dauxois and Pousse, 1976), the sampling model (Dauxois, Fine and Pousse, 1979) and the different mathematical tools (Fine, 1987, Dauxois, Romain and Viguier, 1994) which permit to solve problems encountered in this type of study, and even to obtain asymptotic behaviour of the analyses random elements such as principal components and canonical variables.

## How to cite

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Fine, Jeanne. "Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach.." SORT 27.2 (2003): 165-174. <http://eudml.org/doc/40446>.

@article{Fine2003,
abstract = {Asymptotic study of canonical correlation analysis gives the opportunity to present the different steps of an asymptotic study and to show the interest of an operator and tensor approach of multidimensional asymptotic statistics rather than the classical, matrix and analytic approach. Using the last approach, Anderson (1999) assumes the random vectors to have a normal distribution and the non zero canonical correlation coefficients to be distinct. The new approach we use, Fine (2000), is coordinate-free, distribution-free and permits to have no restriction on the canonical correlation coefficients multiplicity order. Of course, when vectors have a normal distribution and when the non zero canonical correlation coefficients are distinct, it is possible to find again Anderson's results but we diverge on two of them. In this methodological presentation, we insist on the analysis frame (Dauxois and Pousse, 1976), the sampling model (Dauxois, Fine and Pousse, 1979) and the different mathematical tools (Fine, 1987, Dauxois, Romain and Viguier, 1994) which permit to solve problems encountered in this type of study, and even to obtain asymptotic behaviour of the analyses random elements such as principal components and canonical variables.},
author = {Fine, Jeanne},
journal = {SORT},
keywords = {Teoría de la distribución; Distribución asintótica; Análisis multivariante; Análisis de correlación canónica; Operadores; multivariate analysis; canonical correlation analysis; asymptotic study; operator; coordinate-free; distribution-free},
language = {eng},
number = {2},
pages = {165-174},
title = {Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach.},
url = {http://eudml.org/doc/40446},
volume = {27},
year = {2003},
}

TY - JOUR
AU - Fine, Jeanne
TI - Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach.
JO - SORT
PY - 2003
VL - 27
IS - 2
SP - 165
EP - 174
AB - Asymptotic study of canonical correlation analysis gives the opportunity to present the different steps of an asymptotic study and to show the interest of an operator and tensor approach of multidimensional asymptotic statistics rather than the classical, matrix and analytic approach. Using the last approach, Anderson (1999) assumes the random vectors to have a normal distribution and the non zero canonical correlation coefficients to be distinct. The new approach we use, Fine (2000), is coordinate-free, distribution-free and permits to have no restriction on the canonical correlation coefficients multiplicity order. Of course, when vectors have a normal distribution and when the non zero canonical correlation coefficients are distinct, it is possible to find again Anderson's results but we diverge on two of them. In this methodological presentation, we insist on the analysis frame (Dauxois and Pousse, 1976), the sampling model (Dauxois, Fine and Pousse, 1979) and the different mathematical tools (Fine, 1987, Dauxois, Romain and Viguier, 1994) which permit to solve problems encountered in this type of study, and even to obtain asymptotic behaviour of the analyses random elements such as principal components and canonical variables.
LA - eng
KW - Teoría de la distribución; Distribución asintótica; Análisis multivariante; Análisis de correlación canónica; Operadores; multivariate analysis; canonical correlation analysis; asymptotic study; operator; coordinate-free; distribution-free
UR - http://eudml.org/doc/40446
ER -

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