Nonparametric estimation of large covariance matrices with conditional sparsity

Nonparametric estimation of large covariance matrices of longitudinal data

Estimation of an unstructured covariance matrix is difficult because of its positivedefiniteness constraint. This obstacle is removed by regressing each variable on its predecessors, so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying-coefficient and varying-order regression models. Our framework is similar to the use of increasing-ord...

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...

Estimation of Large Covariance Matrices

This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (logp)/n→ 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned fam...

Regularized estimation of large covariance matrices

This paper considers estimating a covariance matrix of p variables from n observations by either banding or tapering the sample covariance matrix, or estimating a banded version of the inverse of the covariance. We show that these estimates are consistent in the operator norm as long as (logp)/n→ 0, and obtain explicit rates. The results are uniform over some fairly natural well-conditioned fam...

Minimax Estimation of Large Covariance Matrices 1369