Adaptive covariance matrix estimation through block thresholding

Adaptive Covariance Matrix Estimation through Block Thresholding

Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance matrix estimation where the goal is to construct a single procedure which is minimax rate optimal simultaneously over each parameter space in a large collectio...

Adaptive Thresholding for Sparse Covariance Matrix Estimation

In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covarianc...

Supplement to “Adaptive Thresholding for Sparse Covariance Matrix Estimation”

Adaptive Wavelet Estimation: A Block Thresholding And Oracle Inequality Approach

We study wavelet function estimation via the approach of block thresholding and ideal adaptation with oracle. Oracle inequalities are derived and serve as guides for the selection of smoothing parameters. Based on an oracle inequality and motivated by the data compression and localization properties of wavelets, an adaptive wavelet estimator for nonparametric regression is proposed and the opti...

Estimation of Covariance Matrix

Estimation of population covariance matrices from samples of multivariate data is important. (1) Estimation of principle components and eigenvalues. (2) Construction of linear discriminant functions. (3) Establishing independence and conditional independence. (4) Setting confidence intervals on linear functions. Suppose we observed p dimensional multivariate samples X1, X2, · · · , Xn i.i.d. wi...