We introduce a Covariance matrix Refitted Cross Validation (CovRCV) estimation procedure without requiring the Gaussian assumption. Specifically, we first usethe modified Cholesky decomposition(MCD) to transform the problem of covariance matrix estimation to that of coefficient estimation in the regression...
Sparse Covariance Matrix EstimationWith Eigenvalue Constraints We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator ... H Liu,LieWANG,T Zhao 被引量: 0发表: 0年 Sparse Estimation of High-Dimensional In...
Covariance matrices play an important role in many multivariate techniques and hence a good covariance estimation is crucial in this kind of analysis. In many applications a sparse covariance matrix is expected due to the nature of the data or for simple interpretation. Hard thresholding, soft ...
(2011). High Dimensional Low Rank and Sparse Covariance Matrix Estimation via ... L Xi - 《General Information》 被引量: 32发表: 2011年 Regularized Estimation of High-dimensional Covariance Matrices By inferringthe block-sparse structures of the high-dimensional covariance matrixfrom a set of ...
The approach not only can easily guarantee the positive definiteness of a covariance matrix, but also transforms the problem of estimating covariance matrices into one that employs m−1 linear regressions. The modified Cholesky decomposition to covariance matrix estimation has been employed in Bickel ...
Keywordsandphrases:Covariancematrix,Highdimensionlowsample size,largepsmalln,Lasso,Sparsity,Choleskydecomposition. ReceivedJanuary2008. ∗ Correspondingauthor,439WestHall,1085S.University,AnnArbor,MI48109-1107. 494 A.J.Rothmanetal./Sparsecovarianceestimation495 ...
We consider the structured covariance matrix estimation and related problems for high-dimensional linear processes. A comprehensive characterization is given for the spectral and the Frobenius norm rates of convergence for the thresholde... X Chen,M Xu,WB Wu 被引量: 3发表: 2015年 Estimating struct...
spectroscopy,climatestudies,financialdata,andmanyothers.Estimationofthecovariancematrix hasalwaysbeenafundamentalprobleminstatisticalinference,sincethecovariancematrixplaysa keyroleinmanydataanalysistechniques.Principalcomponentanalysis(PCA),classificationby linearandquadraticdiscriminantanalysis(LDAandQDA),inferenceabou...
The learning is based on a convex optimization problem, called the sparse inverse covariance estimation, for which many efficient algorithms have been developed in the past few years. When dimensions are much larger than sample sizes, structure learning requires to consider statistical stability, in ...
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of convergence in the ...