Classifying elliptically distributed observations using the Ledoit–Wolf shrinkage approach

Abstract

Classifying observations by the method of linear discriminant analysis deals with two challenges. First, the observations may not follow a Gaussian distribution, Second, the covariance matrix is singular when the number of predictor variables exceeds the number of observations. In this article, we study the classification of high-dimensional elliptically distributed data in the framework of Bayesian approach, while using the Ledoit and Wolf’s shrinkage methodology to overcome the singularity of the covariance matrix. Also, a special case t-distribution is considered and the optimal shrinkage parameter is obtained. Furthermore, we evaluated the performance of the proposed estimators on synthetic and real data. Although the optimal shrinkage parameter does not necessarily provide the minimum test error rate, it can provide a solution to show the superiority of our proposed estimation versus some benchmark method.