Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach
Fine, Jeanne (Université Paul Sabatier (France))

Date:	2003
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 behavior of the analyses random elements such as principal components and canonical variables. ).
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Multivariate analysis ; Canonical correlation analysis ; Asymptotic study ; Operator ; Coordinatefree ; Distribution-free
Published in:	SORT : statistics and operations research transactions, Vol. 27, Núm. 2 (July-December 2003) , p. 165-174, ISSN 2013-8830

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