SHRINKAGE PARAMETER FOR THE MODIFIED LINEAR DISCRIMINANT-ANALYSIS

Linear discriminant analysis is considered in the small-sample and high-dimensional setting. Alternatives to the usual pooled sample estimate of the covariance matrix are discussed. These estimators are characterized by a shrinkage parameter gamma taking its values in [0,1]. We show that the variance of the modified linear discriminant functions is smaller than the variance of the classical linear discriminant function. Moreover, we propose two alternative simple procedures for choosing the shrinkage parameter which are related to the discrimination context. Our procedures are based on the cross-validated misclassification risk and on the cross-validated generalized discriminant function. The optimal value of the shrinkage parameter is computed explicitly. The efficiency of both methods is examined through numerical experiments.