Ensemble sparse estimation of covariance structure for exploring genetic disease data

Abstract

High-dimensional data often occur nowadays in various areas, such as genetic and microarray data. The covariance matrix is of fundamental importance in analyzing the relationship between multivariate variables. A powerful tool for estimating a covariance matrix is the modified Cholesky decomposition, which allows for unconstrained estimation and guarantees the positive definiteness of the estimate. However, it requires a pre-specified ordering of variables before analysis, which is often not available in the real data. Hence, an ensemble Cholesky-based sparse estimation is proposed for a high-dimensional covariance matrix by adopting the model averaging idea. The asymptotically theoretical convergence rate is established under some regularity conditions. The merits of the proposed model are illustrated by the numerical study and two genetic disease data.