Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein's loss

Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein’s loss

In this paper the problem of estimating a covariance matrix parametrized by an irreducible symmetric cone in a decision-theoretic set-up is considered. By making use of some results developed in a theory of finite-dimensional Euclidean simple Jordan algebras, Bartlett’s decomposition and an unbiased risk estimate formula for a general family of Wishart distributions on the irreducible symmetric...

Estimation of Covariance Matrices under Sparsity Constraints

Discussion of “Minimax Estimation of Large Covariance Matrices under L1-Norm” by Tony Cai and Harrison Zhou. To appear in Statistica Sinica. Introduction. Estimation of covariance matrices in various norms is a critical issue that finds applications in a wide range of statistical problems, and especially in principal component analysis. It is well known that, without further assumptions, the em...

Self-Scaled Barriers for Irreducible Symmetric Cones

Self{scaled barrier functions are fundamental objects in the theory of interior{point methods for linear optimization over symmetric cones, of which linear and semideenite programming are special cases. We are classifying all self{scaled barriers over irreducible symmetric cones and show that these functions are merely homothetic transformations of the universal barrier function. Together with ...

Estimation of the Multivariate Normal Mean under the Extended Reflected Normal Loss Function

Minimax Estimation of Large Covariance Matrices under l1-Norm

Driven by a wide range of applications in high-dimensional data analysis, there has been significant recent interest in the estimation of large covariance matrices. In this paper, we consider optimal estimation of a covariance matrix as well as its inverse over several commonly used parameter spaces under the matrix l1 norm. Both minimax lower and upper bounds are derived. The lower bounds are ...