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

Título inglés	Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach.
Título español	Estudio asintótico de análisis de correlación canónica: del enfoque analítico y matricial al enfoque basado en operadores y tensores.
Autor/es	Fine, Jeanne
Organización	Lab. Stat. Probab. Univ. Paul Sabatier, Toulouse, Francia
Revista	1696-2281
Publicación	2003, 27 (2): 165-174, 13 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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.
Clasificación UNESCO	120909
Palabras clave español	Teoría de la distribución ; Distribución asintótica ; Análisis multivariante ; Análisis de correlación canónica ; Operadores
Código MathReviews	MR2036659
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