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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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https://hal.inria.fr/inria-00077033
Contributor : Rapport de Recherche Inria <>
Submitted on : Monday, May 29, 2006 - 11:56:24 AM
Last modification on : Friday, May 25, 2018 - 12:02:06 PM
Long-term archiving on: : Friday, May 13, 2011 - 10:39:07 PM

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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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