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Linear discriminant analysis (LDA) is a typical method for classificationproblems with large dimensions and small samples. There are various types ofLDA methods that are based on the different types of estimators for thecovariance matrices and mean vectors. In this paper, we consider shrinkagemethods based on a non-parametric approach. For the precision matrix, methodsbased on the sparsity structure or data splitting are examined. Regarding theestimation of mean vectors, Non-parametric Empirical Bayes (NPEB) methods andNon-parametric Maximum Likelihood Estimation (NPMLE) methods, also known asf-modeling and g-modeling, respectively, are adopted. The performance of lineardiscriminant rules based on combined estimation strategies of the covariancematrix and mean vectors are analyzed in this study. Particularly, the studypresents a theoretical result on the performance of the NPEB method andcompares it with previous studies. Simulation studies with various covariancematrices and mean vector structures are conducted to evaluate the methodsdiscussed in this paper. Furthermore, real data examples such as geneexpressions and EEG data are also presented

High dimensional discriminant rules with shrinkage estimators of the covariance matrix and mean vector