Slicing: Nonsingular Estimation of High Dimensional Covariance Matrices Using Multiway Kronecker Delta Covariance Structures

摘要

Nonsingular estimation of high dimensional covariance matrices is animportant step in many statistical procedures like classification, clustering,variable selection an future extraction. After a review of the essentialbackground material, this paper introduces a technique we call slicing forobtaining a nonsingular covariance matrix of high dimensional data. Slicing isessentially assuming that the data has Kronecker delta covariance structure.Finally, we discuss the implications of the results in this paper and providean example of classification for high dimensional gene expression data.