  Linear discriminant analysis (LDA) is a typical method for classification
problems with large dimensions and small samples. There are various types of
LDA methods that are based on the different types of estimators for the
covariance matrices and mean vectors. In this paper, we consider shrinkage
methods based on a non-parametric approach. For the precision matrix, methods
based on the sparsity structure or data splitting are examined. Regarding the
estimation of mean vectors, Non-parametric Empirical Bayes (NPEB) methods and
Non-parametric Maximum Likelihood Estimation (NPMLE) methods, also known as
f-modeling and g-modeling, respectively, are adopted. The performance of linear
discriminant rules based on combined estimation strategies of the covariance
matrix and mean vectors are analyzed in this study. Particularly, the study
presents a theoretical result on the performance of the NPEB method and
compares it with previous studies. Simulation studies with various covariance
matrices and mean vector structures are conducted to evaluate the methods
discussed in this paper. Furthermore, real data examples such as gene
expressions and EEG data are also presented
