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.
Mathematics Subject Classification (2000)
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
C. Croux and C. Dehon, Robust Linear Discriminant Analysis using S-estimators. Canad. J. Statist. 29 (2001), 473–492.
C. Croux and G. Haesboeck, Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator. J. Multivariate Anal. 71 (1999), 161–190.
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.
P. L. Davies, Asymptotic Behavior of S-estimators of Multivariate Location Parameters and Dispersion Matrices. Ann. Statist. 15 (1987), 1269–1292.
W. K. Fung, Diagnostics in Linear Discriminant Analysis. J. Amer. Statist. As-soc. 90 (1995), 952–956.
W. K. Fung, Diagnosing Influential Observations in Quadratic Discriminant Analysis. Biometrics 52 (1996), 1235–1241.
D. M. Hawkins and G. J. McLachlan, High Breakdown Linear Discriminant Analysis. J. Amer. Statist. Assoc. 92 (1997), 136–143.
X. He and W. K. Fung, High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis. J. Multivariate Anal. 72 (2000), 151–162.
M. Hubert and K. Van Driessen, Fast and Robust Discriminant Analysis. Comput. Statist. Data Anal. 45 (2004), 301–320.
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.
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.
P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection. Wiley, New York, 1987.
P. J. Rousseeuw and K. Van Driessen, A Fast Algorithm for the Minimum Covariance Determinant Estimator. Technometrics 41 (1999), 212–223.
D. Ruppert, Computing S-estimators for Regression and Multivariate Location/Dispersion. J. Comput. Graph. Statist. 1 (1992), 253–270.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Basel AG
About this paper
Cite this paper
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
Download citation
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