Robustness in Discriminant Analysis
The problems of discriminant analysis in ℝN for L classes are considered for the situations, when hypothetical (classical) model of data is distorted. Classification of distortion types is given. Robustness of classical decision rules is evaluated to the distortions of probability density functions of observations to be classified, and robust decision rules are constructed.
Key words and phrasesDiscriminant analysis types of distortions breakdown point robust decision rule
AMS 1991 subject classificationsPrimary 62H secondary 62C
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- Kadane, J.B. (ed., 1984): Robustness of Bayesian Analysis. North-Holland, New York.Google Scholar
- Kharin, Y.S. (1981): About statistical classification accuracy at MC-estimators using. Probability Theory and Its Applications 26 866–867.Google Scholar
- Kharin, Y.S. (1984): Robustness investigation for the decision rules by risk asymptotic expansion method. In Proceedings of the Third Prague Symposium on Asymptotic Statistics (P. Mandi ed.), 309–317. H.X.-Oxford, Elsevier, Amsterdam.Google Scholar
- Kharin, Y.S. et al. (1991): Asymptotic robustness of discriminant procedures for dependent and non-homogeneous observations. In Probability Theory and Mathematical Statistics 602–610. Proc. of the 5 Vilnius Conf., Utrecht, Netherlands.Google Scholar
- Kharin, Y.S. (1992): Robustness in Statistical Pattern Recognition. Minsk, Universitetskoje.Google Scholar
- Kharin, Y.S. and Zhuk, E.E. (1993): Asymptotic robustness in clusteranalysis for the case of Tukey-Huber distortions. In Information and Classification (Opitz, O., Lausen, B., Klar, R., eds.), 31–39. Springer-Verlag, New York.Google Scholar
- Raudis, S.H. (1976): Sample size finiteness in classification problems. Statistical control problems 18 1–180.Google Scholar