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Empirical Comparison of the Classification Performance of Robust Linear and Quadratic Discriminant Analysis

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Theory and Applications of Recent Robust Methods

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

The aim of this paper is to look at the behavior of the total probability of misclassification of robust linear and quadratic discriminant analysis. The effect of outliers on the discriminant rules is studied by comparing their total probabilities of misclassification in presence of outliers.

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References

  1. C. Croux and C. Dehon, Robust Linear Discriminant Analysis using S-estimators. Canad. J. Statist. 29 (2001), 473–492.

    Article  MathSciNet  MATH  Google Scholar 

  2. C. Croux and G. Haesboeck, Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator. J. Multivariate Anal. 71 (1999), 161–190.

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Croux and K. Joossens, Influence of Observations on the Mis classification Probability in Quadratic Discriminant Analysis. Research Report 59 (2003), Dept. of Applied Economics, K. U. Leuven, Belgium.

    Google Scholar 

  4. P. L. Davies, Asymptotic Behavior of S-estimators of Multivariate Location Parameters and Dispersion Matrices. Ann. Statist. 15 (1987), 1269–1292.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. K. Fung, Diagnostics in Linear Discriminant Analysis. J. Amer. Statist. As-soc. 90 (1995), 952–956.

    Article  MathSciNet  MATH  Google Scholar 

  6. W. K. Fung, Diagnosing Influential Observations in Quadratic Discriminant Analysis. Biometrics 52 (1996), 1235–1241.

    Article  MathSciNet  MATH  Google Scholar 

  7. D. M. Hawkins and G. J. McLachlan, High Breakdown Linear Discriminant Analysis. J. Amer. Statist. Assoc. 92 (1997), 136–143.

    Article  MathSciNet  MATH  Google Scholar 

  8. X. He and W. K. Fung, High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis. J. Multivariate Anal. 72 (2000), 151–162.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Hubert and K. Van Driessen, Fast and Robust Discriminant Analysis. Comput. Statist. Data Anal. 45 (2004), 301–320.

    Article  MathSciNet  MATH  Google Scholar 

  10. R. H. Randies, J. D. Broffitt, J. S. Ramsberg, and R. V. Hogg, Generalized Linear and Quadratic Discriminant Functions using Robust Estimators. J. Amer. Statist. Assoc. 73 (1978), 564–568.

    Article  Google Scholar 

  11. P. J. Rousseeuw, Multivariate Estimation with High Breakdown Point. In W. Gross-mann, G. Pflug, I. Vincze, and W. Wertz, editors, Mathematical Statistics and Applications, vol B, pages 283–297. Reidel Publishing Company, Dordrecht, 1985.

    Chapter  Google Scholar 

  12. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection. Wiley, New York, 1987.

    Book  MATH  Google Scholar 

  13. P. J. Rousseeuw and K. Van Driessen, A Fast Algorithm for the Minimum Covariance Determinant Estimator. Technometrics 41 (1999), 212–223.

    Article  Google Scholar 

  14. D. Ruppert, Computing S-estimators for Regression and Multivariate Location/Dispersion. J. Comput. Graph. Statist. 1 (1992), 253–270.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Applied Economics, Katholieke Universiteit Leuven, Naamsestraat 69, B-3000, Leuven, Belgium

    K. Joossens & C. Croux

Authors
  1. K. Joossens
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  2. C. Croux
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Katholieke Universiteit Leuven, W. de Croylaan 54, 3001, Leuven, Belgium

    Mia Hubert

  2. Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 S9, 9000, Gent, Belgium

    Greet Pison  & Stefan Van Aelst  & 

  3. Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, 2020, Antwerp, Belgium

    Anja Struyf

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© 2004 Springer Basel AG

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Joossens, K., Croux, C. (2004). Empirical Comparison of the Classification Performance of Robust Linear and Quadratic Discriminant Analysis. In: Hubert, M., Pison, G., Struyf, A., Van Aelst, S. (eds) Theory and Applications of Recent Robust Methods. Statistics for Industry and Technology. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7958-3_12

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  • DOI: https://doi.org/10.1007/978-3-0348-7958-3_12

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9636-8

  • Online ISBN: 978-3-0348-7958-3

  • eBook Packages: Springer Book Archive

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