Regularized Discriminant Analysis

References

• Anderson , T. W. 1958 . An Introduction to Multivariate Analysis , New York : John Wiley .
   Google Scholar
• Breiman , L. , Friedman , J. H. , Olshen , R. and Stone , C. J. 1983 . Classification and Regression Trees , Belmont , CA : Wadsworth .
   Google Scholar
• Copas , J. B. 1983 . “Regression, Prediction and Shrinkage” . Journal of the Royal Statistical Society , 45 : 311 – 354 . (with discussion), Ser. B
   Google Scholar
• Cornfield , J. 1967 . “Discriminant Functions,” . Review of the International Statistical Institute , 35 : 142 – 153 .
   Web of Science ®Google Scholar
• Crawford , S. 1986 . “Resampling Strategies for Recursive Partitioning Classification With the CART® Algorithm,” , Stanford University, Dept. of Education . unpublished Ph.D. dissertation
   Google Scholar
• Devlin , S. J. , Gnanadesikan , R. and Kettenring , J. R. 1975 . “Robust Estimation and Outlier Detection With Correlation Coefficients,” . Biometrika , 62 : 531 – 545 .
   Web of Science ®Google Scholar
• Dey , D. K. and Srmivasan , C. 1985 . “Estimation of a Covariance Matrix Under Stein's Loss,” . The Annals of Statistics , 13 : 1581 – 1591 .
   Web of Science ®Google Scholar
• Efron , B. 1983 . “Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation,” . Journal of the American Statistical Association , 78 : 316 – 331 .
   Web of Science ®Google Scholar
• Efron , B. and Morris , C. 1976 . “Multivariate Empirical Bayes and Estimation of Covariance Matrices,” . The Annals of Statistics , 4 : 22 – 32 .
   Web of Science ®Google Scholar
• Enis , P. and Geisser , S. 1974 . “Optimal Predictive Linear Discriminants,” . The Annals of Statistics , 2 : 403 – 410 .
   Web of Science ®Google Scholar
• Geisser , S. 1977 . “Discrimination, Allocatory and Separatory, Linear Aspects,” . In Classification and Clustering , Edited by: Van Ryzin , J. 301 – 330 . New York : Academic Press .
   Google Scholar
• Golub , G. H. and Van Loan , C. F. 1983 . Matrix Computations , Baltimore : Johns Hopkins University Press .
   Google Scholar
• Gong , G. 1982 . “Cross-Validation, the Jackknife, and the Bootstrap: Excess Error Estimation in Forward Logistic Regression,” , Stanford University, Dept. of Statistics . Technical Report 80
   Google Scholar
• Haff , L. R. 1980 . “Empirical Bayes Estimation of the Multivariate Normal Covariance Matrix,” . The Annals of Statistics , 8 : 586 – 597 .
   Web of Science ®Google Scholar
• James , M. 1985 . Classification Algorithms , London : William Collins .
   Google Scholar
• James , W. and Stein , C. “Estimation With Quadratic Loss,” . Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability . Vol. 1 , pp. 361 – 379 . Berkeley : University of California Press .
   Google Scholar
• Kwan , W. and Kowalski , B. R. 1980 . “Data Analysis of Sensory Scores: Evaluations of Panelists and Wine Score Cards,” . Journal of Food Science , 45 : 213 – 216 .
   Web of Science ®Google Scholar
• Lachenbruch , P. A. 1975 . Discriminant Analysis , New York : Hafner Press .
   Google Scholar
• Lin , S. P. and Perlman , M. D. 1984 . “A Monte Carlo Comparison of Four Estimators for a Covariance Matrix,” . In Multivariate Analysis , Edited by: Krishnaiah , P. R. Vol. 6 , 415 – 429 . Amsterdam : North Holland .
   Google Scholar
• Olkin , I. and Sellian , J. B. 1977 . “Estimating Covariances in a Multivariate Normal Distribution,” . In Statistical Decision Theory and Related Topics II , Edited by: Gupta , S. S. and Moore , D. 313 – 326 . New York : Academic Press .
   Google Scholar
• O'Suilivan , F. 1986 . “A Statistical Perspective on Ill-Posed Inverse Problems,” . Statistical Science , 1 : 502 – 527 .
   Google Scholar
• Stein , C. “Estimation of the Mean of a Multivariate Normal Distribution,” . Proceedings of the Prague Symposium on Asymptotic Statistics . pp. 345 – 381 . Karlova , , Czechoslovakia : Prague University Press .
   Google Scholar
• Stein , C. “Reitz Lecture,” . Paper presented at the 38th annual meeting of the Institute of Mathematical Statistics . Atlanta . unpublished
   Google Scholar
• Stein , C. , Efron , B. and Morris , C. 1972 . “Improving the Usual Estimator of a Normal Covariance Matrix,” , Stanford University, Dept. of Statistics . Report 37
   Google Scholar
• Takemura , A. 1984 . “An Orthogonally Invariant Minimax Estimator of the Covariance Matrix of a Multivariate Normal Population,” . Tsukuba Journal of Mathematics , 8 : 367 – 376 .
   Google Scholar
• Titterington , D. M. 1985 . “Common Structure of Smoothing Techniques in Statistics,” . International Statistical Review , 53 : 141 – 170 .
   Web of Science ®Google Scholar
• Wald , P. W. and Kronmal , R. A. 1977 . “Discriminant Functions When Covariances Are Unequal and Sample Sizes Are Moderate,” . Biometrics , 33 : 479 – 484 .
   Web of Science ®Google Scholar