Shrinkage parameter for modified linear discriminant analysis

Abstract : Linear discriminant analysis is considered in the small-sample, high-dimensional setting. Alternatives, shrinkage estimators, to the usual pooled sample estimate of the covariance matrix are discussed. These estimators are characterized by a shrinkage parameter g taking its values. First, we show that the variance of the modified linear discriminant functions is less than those of the classical linear discriminant function. Morever, we propose two alternative simple procedures, for choosing the shrinkage parameter, which are related the discrimiation problem. Our procedures are based-one on the cross-validated misclassification risk and one on the cross-validated generalized discriminant function as defined in Rayens & Greene (1991). The optimal value of the shrinkage parameter is computed explicity. The efficacy of these methods is examined through some simulation studies.
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Rapport
[Research Report] RR-1793, INRIA. 1992
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https://hal.inria.fr/inria-00077033
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Soumis le : lundi 29 mai 2006 - 11:56:24
Dernière modification le : vendredi 25 mai 2018 - 12:02:06
Document(s) archivé(s) le : vendredi 13 mai 2011 - 22:39:07

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  • HAL Id : inria-00077033, version 1

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Abdallah Mkhadri. Shrinkage parameter for modified linear discriminant analysis. [Research Report] RR-1793, INRIA. 1992. 〈inria-00077033〉

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