High-dimensional asymptotic expansions for the distributions of canonical correlations

Journal of Multivariate Analysis

Volumn 100, Issue 1, 2009, Pages 231-242

  Fujikoshi, Yasunori ^a   Sakurai, Tetsuro ^a  

^a CHUO UNIVERSITY   (Japan)

Author keywords

62E20; 62H10; Asymptotic distributions; Canonical correlations; Extended Fisher's z transformation; High dimensional framework; primary; secondary

Indexed keywords

EID: 55049135287     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2008.04.009     Document Type: Article

References (13)

1. Anderson T.W. An Introduction to Multivariate Statistical Analysis. third ed. (2003), John Wiley & Sons, New York
2. Bai Z.D. Methodologies in spectral analysis of large dimensional random matrices: A review. Statist. Sinica 9 (1999) 611-677
3. Bhattacharya R.N., and Ghosh J.K. On the validity of the formal Edgeworth expansion. Ann. Statist. 6 (1978) 434-451
4. Fujikoshi Y. Asymptotic expansions for the distributions of the sample roots under nonnormality. Biometrika 67 (1980) 45-51
5. Johnstone I.M. On the distribution of the largest eigenvalue in principal component analysis. Ann. Statist. 29 (2001) 295-327
6. Ledoit O., and Wolf M. Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size. Ann. Statist. 30 4 (2002) 1081-1102
7. Muirhead R.J. Aspects of Multivariate Statistical Theory (1982), John Wiley & Sons, New York, NY
8. Raudys S., and Young D.M. Results in statistical discriminant analysis: A review of the former Soviet Union literature. J. Multivariate Anal. 89 (2004) 1-35
9. Schott J.R. Testing for complete independence in high dimensions. Biometrika 92 (2005) 951-956
10. Siotani M. An Introduction to Multivariate Analysis (1990), Asakura-shoten, Tokyo (in Japanese)
11. Siotani M., Hayakawa T., and Fujikoshi Y. Modern Multivariate Statistical Analysis: A Graduate Course and Handbook (1985), American Sciences Press, Columbus, OH
12. Sugiura N., and Fujikoshi Y. Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence. Ann. Math. Statist. 40 3 (1969) 942-952
13. Srivastava M.S. Methods of Multivariate Statistics (2002), John Wiley & Sons, New York