Generalized separation theorems for singular values of a matrix and their applications in canonical correlation analysis

• Autorzy: Xie C. , Singh R. S. , Smith B. , Lu X.
• Języki publikacji: EN

Abstrakty

EN

Rao (1979) established separation theorems for singular values of a matrix and showed their applications in multivariate analysis. In this paper, we provide generalized separation theorems for singular values of a matrix and use them to find some interesting relations between canonical correlations and conditional canonical correlations.

Słowa kluczowe

EN

canonical correlations; conditional canonical correlations; singular values

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2005
• Tom: Vol. 25, Fasc. 2
• Strony: 223--229
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Xie C.

• PHRI, Department of Medicine, McMaster University, Hamilton, Ontario, L8L 2x2, Canada

autor

Singh R. S.

• Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario, N1G 2W1, Canada

autor

Smith B.

• Department of Mathematics & Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5, Canada

autor

Lu X.

• Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada

Bibliografia

• [1] I. M. Gel’fand and M. A. Naimark, The relation between the unitary representations of the complex unimodular group and its unitary subgroup, Izv. Akad. Nauk SSSR Ser. Mat. 14 (1950), pp. 239-260.
• [2] C. R. Rao, Separation theorems for singular values of matrices and their applications in multivariate analysis, J. Multivariate Anal. 9 (1979), pp. 362-377.
• [3] M. S. Srivastava and E. M. Carter, An introduction to Applied Multivariate Statistics, North-Holland, New York 1983.