References
- Ahn , J. , Marron , J. S. , Muller , K. E. and Chi , Y. Y. 2007 . The high-dimension, low-sample-size geometric representation holds under mild conditions . Biometrika , 94 : 760 – 766 .
- Anderson , T. W. 2004 . An Introduction to Multivariate Statistical Analysis. 3rd ed , New York : Wiley .
- Baik , J. , Ben , A. G. and Peche , S. 2005 . Phase transition of the largest eigenvalue for non-null complex covariance matrices . Annals of Probability , 33 : 1643 – 1697 .
- Baik , J. and Silverstein , J. W. 2006 . Eigenvalues of large sample covariance matrices of spiked population models . Journal of Multivariate Analysis , 97 : 1382 – 1408 .
- Cascio , C. J. , Gribbin , M. J. , Gouttard , S. , Smith , R. G. , Jomier , M. , Poe , M. D. , Graves , M. , Hazlett , H. C. , Muller , K. E. , Gerig , G. and Piven , J. 2013 . Decreased variability of fractional anisotropy in young children with autism . Manuscript submitted for publication
- Hall , P. , Marron , J. S. and Neeman , A. 2005 . Geometric representation of high dimension, low sample size data . Journal of the Royal Statistical Society, Series B , 67 : 427 – 444 .
- Johnson , N. L. and Kotz , S. 1972 . Distributions in Statistics: Continuous Multivariate Distributions , New York : Wiley .
- Johnstone , I. M. 2001 . On the distribution of the largest eigenvalue in principal components analysis . Annals of Statistics , 29 : 295 – 327 .
- Johnstone , I. M. and Lu , A. Y. 2009 . On consistency and sparsity for principal components analysis in high dimensions . Journal of the American Statistical Association , 104 : 682 – 693 .
- Jung , S. and Marron , J. S. 2009 . PCA consistency in high dimension, low sample size context . The Annals of Statistics , 37 : 4104 – 4130 .
- Khatri , C. G. 1976 . A note on multiple and canonical correlation for a singular covariance matrix . Psychometrika , 41 : 465 – 470 .
- MacCallum , R. C. , Widaman , K. F. , Zhang , S. and Hong , S. 1999 . Sample size in factor analysis . Psychological Methods , 4 : 84 – 99 .
- Mardia , K. V. , Kent , J. T. and Bibby , J. M. 1979 . Multivariate Analysis , London : Academic Press, Inc .
- Muller , K. E. and Stewart , P. W. 2006 . Linear Model Theory for Univariate, Multivariate and Mixed Models , New York : Wiley .
- Preacher , K. J. and MacCallum , R. C. 2002 . Exploratory factor analysis in behavior genetics research: factor recovery with small sample sizes . Behavior Genetics , 32 : 153 – 161 .
- Rao , M. , Stough , J. , Chi , Y. Y. , Muller , K. E. , Tracton , G. S. , Pizer , S. M. and Chaney , E. L. 2005 . Comparison of human and automatic segmentations of kidneys from CT images . International Journal of Radiation Oncology, Biology and Physics , 61 : 954 – 960 .
-
SAS Institute.
1999
.
SAS/IML
Software , Cary, North Carolina : SAS Institute .
- Srivastava , M. S. 2007 . Multivariate theory for analyzing high dimensional data . Journal of Japanese Statistical Society , 37 : 53 – 86 .
- Srivastava , M. S. and Du , M. 2008 . A test for the mean vector with fewer observations than the dimension . Journal of Multivariate Analysis , 99 : 386 – 402 .
- Srivastava , M. S. and Fujikoshi , Y. 2006 . Multivariate analysis of variance with fewer observations than the dimension . Journal of Multivariate Analysis , 97 : 1927 – 1940 .
- Uhlig , H. 1994 . On singular Wishart and singular multivariate beta distributions . Annals of Statistics , 22 : 395 – 405 .
- Warton , D. I. 2008 . Penalized normal likelihood and ridge regularization of correlation and covariance matrices . Journal of the American Statistical Association , 103 : 340 – 349 .
- Widaman , K. F. 1993 . Common factor analysis versus principal component analysis: differential bias in representing model parameters? . Multivariate Behavioral Research , 28 : 263 – 311 .