Correlation and high-dimensional consistency in pattern recognition

Journal of the American Statistical Association

Volumn 93, Issue 443, 1998, Pages 995-1006

  Ge, Nanxiang ^a   Simpson, Douglas G ^b  

^a Rio Grande Medical Technologies   (United States)

^b UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Euclidean classifier; Exponential error bound; Normalization; Repeated measures

Indexed keywords

EID: 0032326669     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1998.10473762     Document Type: Article

References (28)

1. Bahadur, R. R. (1971), Some IJmit Theorems in Statistics, Philadelphia: SIAM.
2. Bensmail, H., and Celeux, G. (1996), "Regularized Gaussian Discriminant Analysis Through Eigenvalue Decomposition," Journal of the American Statistical Association, 91 1743-1748.
3. Breiman, L., and Freedman, D. (1983), "How Many Variables Should Be Entered in a Regression Equation?" Journal of the American Statistical Association, 78 131-139.
4. Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London: Chapman and Hall.
5. Currie, L. A., Stafford, T. W., Sheffield, A. E., Klouda, G. A., Wise, S. A., Fletcher, R. A., Donohue, D. J., Jull, A. J. T., and Linick, T. W. (1989), "Microchemical and Molecular Dating," Radiocarbon, 31. 448-463.
6. Dawid, A. P., and Fang, B. Q. (1992), "Conjugate Bayes Discrimination With Infinitely Many Variables" Journal of Multivariate Analysis, 41, 27-42.
7. Decvc, A. D. (1970), "Representation of Statistics of Discriminant Analysis and Asymptotic Expansions When Space Dimensions Are Comparable With Sample Size," Soviet Mathematical Doklsum, 11, 1547-1550.
8. Donoho, D. L., and Johnstone, I. M. (1995), "Adapting to Unknown Smoothness via Wavelet Shrinkage," Journal of the American Statistical Association, 90, 1200-1224.
9. Fang, B. Q., and Dawid, A. P. (1993), "Asymptotic Properties of Conjugate Bayes Discrete Discrimination," Journal of Multivariate Analysis, 46, 83-96.
10. Jain, A. K., and Chandrasekaran, B. (1982), "Dimensionality and Sample Size Considerations in Pattern Recognition Practice," Classification, Pattern Recognition and Reduction of Dimensionality, Handbook of Statistics, Vol. 2, eds. P. R. Krishnaiah and L. N. Kanal, Amsterdam; North Holland, pp. 835-855.
11. Kokolakis, G. E. (1981), "On the Expected Probability of Correct Classification," Biometrika, 68, 477-483.
12. Kokolakis, G. E. (1985), "A Martingale Approach to the Problem of Dimensionality and Performance of Bayesian Classifiers: Asymptotic Results," Communications in Statistics, Pan A-Theory and Methods, 14, 927-935.
13. Lindley, D. (1978), "The Bayesian Approach," Scandinavian Journal of Statististics, 5, 1-26.
14. Marco, V. R., Young, D. M., and Turner, D. W. (1987), 'The Euclidean Distance Classifier: An Alternative to the Linear Discriminant Function," Communications in Statistics, Part B-Simulation and Computation, 16, 485-505.
15. Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979), Multivariate Analysis, London: Academic Press.
16. McLachlan, G. J. (1992), Discriminant Analysis and Statistical Pattern Recognition, New York: Wiley.
17. McLachlan, G. J. (1972), "Asymptotic Expansion for the Variance of the Errors of Misclassification of the Linear Discriminant Function," The Australian Journal of Statististics, 14, 68-72.
18. Neyman, J., and Scon, E. L. (1948), "Consistent Estimates Based on Partially Consistent Observations," Econometrica, 16, 1-32.
19. Portnoy, S. (1984), "Asymptotic Behavior of Af-Estimators of Pregression Parameters When p2/n is Large. I. Consistency," The Annals of Statistics, 12, 1298-1309.
20. Raynes, W., and Greene, T., (1991), "Covariance Pooling and Stabilization for Classification," Computational Statistics & Data Analysis, 11,17-42.
21. Saranadasa, H. (1993), "Asymptotic Expansion of Misclassification Probabilities of D-and A-Criteria for Discrimination From Two High Dimensional Populations Using the Theory of Large Dimensional Matrices," Journal of Multivariate Analysis, 46, 154-174.
22. Schervish, M. J. (1981), "Asymptotic Expansions for Correct Classification Rates in Discriminant Analysis," Annals of Statistics, 9, 1002-1009.
23. Serfling, R. J. (1980), Approximation Theorems of Mathematical Statistics, Series in Probability and Mathematical Statistics. New York: Wiley.
24. Simpson, D. G., Guo, S., Sacks, J., Bietz, J. A., Huebner, F., and Nelsen, T. (1991). "Relating Chromatographic Data to Measurements of Wheat Quality: Case Studies in Dimensions Reductions." Chemometrics and Intelligent laboratory Systems, 10, 155-167.
25. Sutradhar, B. C. (1990), "Discrimination of Observations Into One of Two t Populations," Biometrics, 46, 827-835
26. Raudys, S., and Pikelis, V. (1980), "On Dimensionality, Sample Size, Classification Error, and Complexity of Classification Algorithm in Pattern Recognition," IEEE Transactions on Pattern Analysis and Machine Intelligence. PAM 1-2, 242-252.
27. Varmuza, K. (1992), "Chemometrics in Mass Spectrometry," International Journal of Mass Spectrometry and Ion Processes, 118/119, 811-823.
28. Wold, S., Martens, H., and Wold, H. (1983), 'The Multivariate Calibration Problem in Chemistry Solved by the PLS Method," Matrix Pencils. Proceedings of a Conference Held at Pite Havsbad, March 22-24, 1982. eds. A. Ruhe and B. Kagstrom. Lecture Notes in Mathematics 973, Heidelberg: Springer-Verlag. pp. 286-293.