High-Dimensional Quadratic Classifiers in Non-sparse Settings

In this paper, we consider high-dimensional quadratic classifiers in non-sparse settings. The quadratic classifiers proposed in this paper draw information about heterogeneity effectively through both the differences of growing mean vectors and covariance matrices. We show that they hold a consistency property in which misclassification rates tend to zero as the dimension goes to infinity under non-sparse settings. We also propose a quadratic classifier after feature selection by using both the differences of mean vectors and covariance matrices. We discuss the performance of the classifiers in numerical simulations and actual data analyzes. Finally, we give concluding remarks about the choice of the classifiers for high-dimensional, non-sparse data.