Exact representation of the second-order moments for resubstitution and leave-one-out error estimation for linear discriminant analysis in the univariate heteroskedastic Gaussian model

Pattern Recognition

Volumn 45, Issue 2, 2012, Pages 908-917

  Zollanvari, Amin ^a,b,c   Braga Neto, Ulisses ^d   Dougherty, Edward R ^d,e,f  

^a HARVARD MIT DIVISION OF HEALTH SCIENCES AND TECHNOLOGY   (United States)

^b BRIGHAM AND WOMEN S HOSPITAL   (United States)

^c HARVARD MEDICAL SCHOOL   (United States)

^d Texas AandM University   (United States)

^e TRANSLATIONAL GENOMICS RESEARCH INSTITUTE   (United States)

^f UNIVERSITY OF TEXAS MD ANDERSON CANCER CENTER   (United States)

Author keywords

Error estimation; Genomics; Heteroskedasticity; Leave one out; Linear discriminant analysis; Resubstitution; RMS

Indexed keywords

GENOMICS; HETEROSKEDASTICITY; LEAVE-ONE-OUT; LINEAR DISCRIMINANT ANALYSIS; RESUBSTITUTION; RMS;

DISCRIMINANT ANALYSIS; ERROR ANALYSIS; ESTIMATION; PROBABILITY; SAMPLING;

GAUSSIAN DISTRIBUTION;

EID: 80052964854     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2011.08.006     Document Type: Article

References (29)

1. M. Hills Allocation rules and their error rates Journal of the Royal Statistical Society. Series B (Methodological) 1 1966 1 31
2. G.J. McLachlan An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis Australian Journal of Statistics 15 3 1973 210 214
3. N. Glick Additive estimators for probabilities of correct classification Pattern Recognition 10 1978 211 222 (Pubitemid 9029903)
4. K. Fukunaga, and R.R. Hayes Estimation of classifier performance IEEE Transactions on Pattern Analysis and Machine Intelligence 11 1989 1087 1101 (Pubitemid 20628923)
5. U. Braga-Neto, and E. Dougherty Is cross-validation valid for microarray classification? Bioinformatics 20 3 2004 374 380
6. S. Raudys Statistical and Neural Classifiers, An Integrated Approach to Design 2001 Springer-Verlag London
7. L. Devroye, and T. Wagner Distribution-free inequalities for the deleted and hold-out error estimates IEEE Transactions on Information Theory 25 1979 202 207 (Pubitemid 9443301)
8. L. Devroye, and T. Wagner Distribution-free performance bounds for potential function rules IEEE Transactions on Information Theory 25 1979 601 604 (Pubitemid 10426456)
9. D. Foley Considerations of sample and feature size IEEE Transactions on Information Theory IT-18 1972 618 626
10. N. Glick Sample-based multinomial classification Biometrics 29 1973 241 256
11. M. Goldstein, and E. Wolf On the problem of bias in multinomial classification Biometrics 33 1977 325 331 (Pubitemid 8131510)
12. U.M. Braga-Neto, and E.R. Dougherty Exact correlation between actual and estimated errors in discrete classification Pattern Recognition Letters 31 2010 407 413
13. U.M. Braga-Neto, and E.R. Dougherty Exact performance measures and distributions of error estimators for discrete classifiers Pattern Recognition 38 2005 1799 1814
14. A. Zollanvari, U. Braga-Neto, and E. Dougherty On the sampling distribution of resubstitution and leave-one-out error estimators for linear classifiers Pattern Recognition 42 2009 2705 2723
15. A. Zollanvari, U. Braga-Neto, and E. Dougherty Joint sampling distribution between actual and estimated classification errors for linear discriminant analysis IEEE Transaction on Information Theory 56 2 2010 784 804
16. F.H. Schršder, J. Hugosson, and M.J. Roobol Screening and prostate-cancer mortality in a randomized European study New England Journal of Medicine 360 2009 1320 1328
17. C.J.L. Koelinka, P. van Hasseltb, A. van der Ploegc, M.M. van den Heuvel-Eibrinkd, F.A. Wijburge, C.M.A. Bijlevelda, and F.J. van Spronsen Tyrosinemia type I treated by NTBC: How does AFP predict liver cancer? Molecular Genetics and Metabolism 89 2006 310 315
18. R.C.J. Bast, F.J. Xu, Y.H. Yu, S. Barnhill, Z. Zhang, and G.B. Mills Ca 125: the past and the future International Journal of Biological Markers 13 1998 179 187 (Pubitemid 29178546)
19. X. Filella, R. Molina, J.J. Grau, J.M. PiquŽ, J.C. Garcia-Valdecasas, E. Astudillo, A. Biete, J.M. Bordas, A. Novell, and E. Campo Prognostic value of Ca 19.9 levels in colorectal cancer Molecular Genetics and Metabolism 216 1992 55 59
20. T.S. Frank, A.M. Deffenbaugh, J.E. Reid, M. Hulick, B.E. Ward, B. Lingenfelter, K.L. Gumpper, T. Scholl, S.V. Tavtigian, D.R. Pruss, and G.C. Critchfield Clinical characteristics of individuals with germline mutations in BRCA1 and BRCA2: analysis of 10,000 individuals Journal of Clinical Oncology 20 2002 1480 1490 (Pubitemid 34260526)
21. K. Syrjakoski, T. Kuukasjarvi, K. Waltering, K. Haraldsson, A. Auvinen, A. Borg, T. Kainu, O. Kallioniemi, and P.A. Koivisto BRCA2 mutations in 154 Finnish male breast cancer patients Neoplasia 6 2004 541 545 (Pubitemid 39411091)
22. A. Horii, S. Nakatsuru, Y. Miyoshi, S. lchii, H. Nagase, H. Ando, A. Yanagisawa, E. Tsuchiya, Y. Kato, and Y. Nakamura Frequent somatic mutations of the APC gene in human pancreatic cancer Cancer Research 52 1992 6696 6698
23. C. Smith Some examples of discrimination Annals of Eugenics 18 1947 272 282
24. P. Lachenbruch, and M. Mickey Estimation of error rates in discriminant analysis Technometrics 10 1968 1 11
25. A. Zollanvari, U. Braga-Neto, and E. Dougherty On the sampling distribution of resubstitution and leave-one-out error estimators for linear classifiers Pattern Recognition 42 11 2009 2705 2723
26. S.J. Raudys, and A.K. Jain Small sample size effects in statistical pattern recognition: recommendations for practitioners IEEE Transactions on Pattern Analysis and Machine Intelligence 13 1991 252 264
27. S. Raudys, and V. Pikelis On dimensionality, sample size, classification error, and complexity of classification algorithm in pattern recognition IEEE Transactions on Pattern Analysis and Machine Intelligence 2 1980 242 252 (Pubitemid 10485853)
28. L. Devroye, L. Gyorfi, and G. Lugosi A Probabilistic Theory of Pattern Recognition 1996 Springer New York
29. M. van de Vijver, and Y. He A gene-expression signature as a predictor of survival in breast cancer The New England Journal of Medicine 347 2002 1999 2009 (Pubitemid 35461656)