[en] Linear and Quadratic Discriminant Analysis (LDA/QDA) are the most often applied classification rules under the normality assumption. When there is not enough data, the quadratic rule, which requires the estimation of one precision matrix in each class, is often replaced by the linear one, based on the homoscedasticity assumption. This strong assumption is however rarely verified in practice and ignores the intrinsic différences between groups that may be of particular interest in the classification context. In this aper, alternatives to the usual maximum likelihood estimates for the precision matrices are proposed that borrow strength across classes while allowing for heterogeneity at the same time. This results in a classifier that is intermediate between QDA and LDA. Moreover, our estimator is sparse: the undesirable effect of uninformative variables is reduced. The performance of the method is illustrated through simulated and real dataset
examples.
Disciplines :
Mathematics
Author, co-author :
Aerts, Stéphanie ; Université de Liège > HEC-Ecole de gestion : UER > UER Opérations : Informatique de gestion
Croux, Christophe; Katholieke Universiteit Leuven - KUL > Faculty of Economics and Business > ORSTAT
Wilms, Ines; Katholieke Universiteit Leuven - KUL > Faculty of Economics and Business > ORSTAT
Language :
English
Title :
Robust discriminant analysis based on the joint graphical lasso estimator