High dimensional discriminant rules with shrinkage estimators of covariance matrix and mean vector
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Linear discriminant analysis is a typical method used in the case of large dimension and small samples. There are various types of linear discriminant analysis methods, which are based on the estimations of the covariance matrix and mean vectors. Although there are many methods for estimating the inverse matrix of covariance and the mean vectors, we consider shrinkage methods based on non-parametric approach. In the case of the precision matrix, the methods based on either the sparsity structure or the data splitting are considered. Regarding the estimation of mean vectors, nonparametric empirical Bayes (NPEB) estimator and nonparametric maximum likelihood estimation (NPMLE) methods are adopted which are also called f-modeling and g-modeling, respectively. We analyzed the performances of linear discriminant rules which are based on combined estimation strategies of the covariance matrix and mean vectors. In particular, we present a theoretical result on the performance of the NPEB method and compare that with the results from other methods in previous studies. We provide simulation studies for various structures of covariance matrices and mean vectors to evaluate the methods considered in this paper. In addition, real data examples such as gene expressions and EEG data are presented.
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