Asymptotic results in canonical discriminant analysis when the dimension is large compared to the sample size

Journal of Statistical Planning and Inference

Volumn 138, Issue 11, 2008, Pages 3457-3466

  Fujikoshi, Yasunori ^a   Himeno, Tetsuto ^b   Wakaki, Hirofumi ^b  

^a CHUO UNIVERSITY   (Japan)

^b HIROSHIMA UNIVERSITY   (Japan)

Author keywords

Asymptotic null and non null distributions; Canonical discriminant analysis; Characteristic roots; High dimensional framework; Tests for dimensionality

Indexed keywords

EID: 49049090334     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2006.09.028     Document Type: Article

References (12)

1. Anderson T.W. The asymptotic distribution of certain characteristic roots and vectors. In: Neyman J. (Ed). Proceedings of the Second Berkerley Symposium on Mathematical Statistics and Probability (1951), University of California, Berkeley 105-130
2. Anderson T.W. Asymptotic theory for principal component analysis. Ann. Math. Statist. 34 (1963) 122-148
3. Bai Z.D. Methodologies in spectral analysis of large dimensional random matrices, a review. Statist. Sinica 9 (1999) 611-677
4. Bickel P.J., and Levina E. Some theory for Fisher's linear discriminant function, "naive Bayes", and some alternatives when there are more variables than observations. Bernoulli 10 (2004) 989-1010
5. Fujikoshi Y. Asymptotic expansions for the distributions of some multivariate tests. In: Krishnaiah P.R. (Ed). Multivariate Analysis-IV (1977), North-Holland, Amsterdam 55-71
6. Hsu P.L. On the limiting distribution of roots of a determinantal equation. J. London Math. Soc. 16 (1941) 183-194
7. Johnstone I.M. On the distribution of the largest eigenvalue in principal component analysis. Ann. Statist. 29 (2001) 295-327
8. Lawley D.N. Tests of significance for the latent roots of covariance and correlation matrices. Biometrika 43 (1956) 128-136
9. Lawley D.N. Tests of significance in canonical analysis. Biometrika 46 (1959) 59-66
10. 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
11. Siotani M., Hayakawa T., and Fujikoshi Y. Modern Multivariate Statistical Analysis: A Graduate Course and Handbook (1985), American Sciences Press, Columbus, Ohio
12. Wakaki, H., Fujikoshi, Y., Ulyanov, V.V., 2006. Asymptotic expansions of the distributions of MANOVA tests when the dimension is large, submitted for publication.