Stein’s method in high dimensional classification and applications

Abstract

In the context of classification, it is a common phenomenon that high-dimensional data such as micro-array data consist of only a few informative components. If one uses standard statistical modeling and estimation procedures with entire information, it tends to overfit the data due to noise information. Therefore, some regularization conditions are required to select important information. A class of regularization methods is proposed through various shrinkage estimators using Stein’s identity. Since hard thresholding does not satisfy the condition of Stein’s identity, the proposed methods consider linear classifiers with soft, firm and SCAD thresholdings incorporating Stein’s identity and show some asymptotic properties. Simulation studies and applications to three different micro array data sets show that the proposed methods work well. Also the proposed methods are compared with some existing methods.