In this paper we propose a new regression interpretation of the Cholesky factor of the covariance matrix, as opposed to the well-known regression interpretation of the Cholesky factor of the inverse covariance, which leads to a new class of regularized covariance estimators suitable for high-dimensional problems. Regularizing the Cholesky factor of the covariance via this regression interpretat...

The following notational conventions and terminology will be in force. Inequalities for vectors are understood component-wise. Given two matrices M and N with the same number of columns, the notation col(M, N) denotes the matrix obtained by stacking M over N. Let M be a matrix. The sub-matrix M JK of M is the matrix whose entries lie in the rows of M indexed by the set J and the columns indexed...