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Original Articles

Rank-Based Classification Using Robust Discriminant Functions

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Pages 199-214 | Received 12 Aug 2008, Accepted 02 Sep 2008, Published online: 25 Nov 2008

References

  • Alon , U. , Barkai , N. , Notterman , D. A. , Gish , K. , Ybarra , S. , Mack , D. , Levine , A. J. ( 1999 ). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays . Proceedings of the National Academy of Science USA 96 ( 12 ): 6745 – 6750 .
  • Billor , N. , Abebe , A. , Turkmen , A. , Nudurupati , S. V. ( 2008 ). Classification based on depth transvariations . Journal of Classification DOI: 10.1007/s00357-008-9015-7 .
  • Crimin , K. , McKean , J. W. , Sheather , S. J. ( 2007 ). Discriminant procedures based on efficient robust discriminant coordinates . Journal of Nonparametric Statistics 19 ( 4–5 ): 199 – 213 .
  • Croux , C. , Dehon , C. ( 2001 ). Robust linear discriminant analysis using S-estimators . Canadian Journal of Statistics 29 ( 3 ): 473 – 493 .
  • Croux , C. , Joossens , K. ( 2005 ). Influence of observations on the misclassification probability in quadratic discriminant analysis . Journal of Multivariate Analysis 96 ( 2 ): 384 – 403 .
  • Croux , C. , Filzmoser , P. , Joossens , K. (2008). Classification efficiencies for robust linear discriminant analysis. Statistica Sinica 18(2):581–599.
  • Dudoit , S. , Fridlyand , J. , Speed , T. P. ( 2002 ). Comparison of discrimination methods for the classification of tumors using gene expression data . Journal of the American Statistical Association 97 ( 457 ): 77 – 87 .
  • Fisher , R. A. ( 1936 ). The use of multiple measurements in taxonomic problems . Annals of Eugenics VII(II) : 179 – 188 .
  • Ghosh , A. K. , Chaudhuri , P. ( 2005 ). On maximum depth and related classifiers . Scandanavian Journal of Statistics 32 ( 2 ): 327 – 350 .
  • Golub , T. R. , Slonim , D. K. , Tamayo , P. , Huard , C. , Gaasenbeek , M. , Mesirov , J. P. , Coller , H. , Loh , M. L. , Downing , J. R. , Caligiuri , M. A. , Bloomfield , C. D. , Lander , E. S. ( 1999 ). Molecular classification of cancer: class discovery and class prediction by gene expression monitoring . Science 286 : 531 – 537 .
  • He , X. , Fung , W. K. ( 2000 ). High breakdown estimation for multiple populations with applications to discriminant analysis . Journal of Multivariate Analysis 72 ( 2 ): 151 – 162 .
  • Hettmansperger , T. P. , McKean , J. W. ( 1998 ). Robust Nonparametric Statistical Methods . Vol. 5. Kendall's Library of Statistics . London : Edward Arnold .
  • Hettmansperger , T. P. , Randles , R. H. ( 2002 ). A practical affine equivariant multivariate median . Biometrika 89 ( 4 ): 851 – 860 .
  • Huber , P. J. ( 1977 ). Robust covariances . In: Statistical Decision Theory and Related Topics, II (Proceedings of the Symposium at Purdue University, Lafayette, Indiana, 1976) . New York : Academic Press , pp. 165 – 191 .
  • Hubert , M. , Van Driessen , K. ( 2004 ). Fast and robust discriminant analysis . Computational Statistics and Data Analysis 45 ( 2 ): 301 – 320 .
  • Hugg , J. , Rafalin , R. , Seyboth , K. , Souvaine , D. ( 2006 ). An experimental study of old and new depth measures . In: Workshop on Algorithm Engineering and Experiments (ALENEX06) . Lecture Notes in Computer Science . New York : Springer-Verlag , pp. 51 – 64 .
  • Johnson , N. L. ( 1949 ). Systems of frequency curves generated by methods of translation . Biometrika 36 : 149 – 176 .
  • Joossens , K. , Croux , C. ( 2004 ). Empirical comparison of the classification performance of robust linear and quadratic discriminant analysis . In: Theory and Applications of Recent Robust Methods . Stat. Ind. Technol. Basel : Birkhäuser , pp. 131 – 140 .
  • Jörnsten, R. ( 2004 ). Clustering and classification based on the L 1 data depth . Journal of Multivariate Analysis 90 ( 1 ): 67 – 89 .
  • Lachenbruch , P. A. ( 1975 ). Discriminant Analysis . New York : Hafner Press .
  • Lachenbruch , P. A. , Sneeringer , C. , Revo , L. T. ( 1973 ). Robustness of the linear and quadratic discriminant function to certain types of non-normality . Communications in Statistics 1 ( 1 ): 39 – 56 .
  • Montanari , A. ( 2004 ). Linear discriminant analysis and transvariation . Journal of Classification 21 ( 1 ): 71 – 88 .
  • Ng , T. H. , Randles , R. H. ( 1983 ). Rank procedures in many population forced discrimination problems . Communications in Statistics A—Theory and Methods 12 ( 17 ): 1943 – 1959 .
  • Nguyen , D. V. , Rocke , D. M. ( 2002 ). Tumor classification by partial least squares using microarray gene expression data . Bioinformatics 18 : 39 – 50 .
  • Nudurupati , S. V. , Abebe , A. ( 2008 ). A nonparametric allocation scheme for classification based on transvariation probabilities . Journal of Statistical Computation and Simulation (in press) .
  • Randles , R. H. , Broffitt , J. D. , Ramberg , J. S. , Hogg , R. V. ( 1978a ). Discriminant analysis based on ranks . Journal of the American Statistical Association 73 ( 362 ): 379 – 384 .
  • Randles , R. H. , Broffitt , J. D. , Ramberg , J. S. , Hogg , R. V. ( 1978b ). Generalized linear and quadratic discriminant functions using robust estimates . Journal of the American Statistical Association 73 ( 363 ): 564 – 568 .
  • Rousseeuw , P. J. (1984). Least median of squares regression. Journal of the American Statistical Association 79(388):871–880.
  • Rousseeuw , P. ( 1985 ). Multivariate estimation with high breakdown point . In: Mathematical Statistics and Applications . Vol. B (Bad Tatzmannsdorf, 1983) . Dordrecht : Reidel , pp. 283 – 297 .
  • Rousseeuw , P. , Van Driessen , K. ( 1999 ). A fast algorithm for the minimum covariance determinant estimator . Technometrics 41 ( 3 ): 212 – 223 .
  • Tyler , D. E. ( 1987 ). A distribution-free M-estimator of multivariate scatter . The Annals of Statistics 15 ( 1 ): 234 – 251 .
  • Vardi , Y. , Zhang , C.-H. ( 2000 ). The multivariate L 1-median and associated data depth . Proceedings of the National Academy of Science USA 97 ( 4 ): 1423 – 1426 (electronic) .
  • Zuo , Y. , Serfling , R. ( 2000 ). General notions of statistical depth function . The Annals of Statistics 28 ( 2 ): 461 – 482 .

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