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.
翻译:在大尺寸和小样品的情况下,线性分布式分析是一种典型的方法,在大尺寸和小样品的情况下,使用线性分布式分析方法,有各种类型的线性分布式分析方法,这些方法基于对共变矩阵和中值矢量的估计,虽然有许多方法用于估计共变矩阵和中值矢量的反矩阵,但我们认为,基于非参数方法的缩小式分析方法;在精确矩阵的情况下,考虑以宽度结构或数据分离为基础的方法;关于平均矢量的估计,采用了非参数性经验性贝斯(NPEB)估计值和非参数性最大概率估计法(NPMLE),这些方法也分别称为模型和模型。我们分析了基于共变矩阵和中值矢量综合估计战略的线性差异性规则的性能。特别是,我们从理论角度分析了 NPEB方法的性能,并将该方法与其他方法的结果进行了比较。我们为各种共变矩阵结构和平均最大可能性估计法度方法提供了模拟研究。我们为实际使用的EEG格式提供了模拟研究。