Eigenvalue Distribution of a High-Dimensional Distance Covariance Matrix With Application

Sparse Covariance Matrix Estimation With Eigenvalue Constraints.

We propose a new approach for estimating high-dimensional, positive-definite covariance matrices. Our method extends the generalized thresholding operator by adding an explicit eigenvalue constraint. The estimated covariance matrix simultaneously achieves sparsity and positive definiteness. The estimator is rate optimal in the minimax sense and we develop an efficient iterative soft-thresholdin...

High dimensional covariance matrix estimation using a factor model

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to∞ as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observab...

Random matrix theory and estimation of high-dimensional covariance matrices

This projects aims to present significant results of random matrix theory in regards to the principal component analysis, including Wigner’s semicircular law and Marčenko-Pastur law describing limiting distribution of large dimensional random matrices. The work bases on the large dimensional data assumptions, where both the number of variables and sample size tends to infinity, while their rati...

High Dimensional Inverse Covariance Matrix Estimation via Linear Programming

This paper considers the problem of estimating a high dimensional inverse covariance matrix that can be well approximated by “sparse” matrices. Taking advantage of the connection between multivariate linear regression and entries of the inverse covariance matrix, we propose an estimating procedure that can effectively exploit such “sparsity”. The proposed method can be computed using linear pro...

Approaches to High-Dimensional Covariance and Precision Matrix Estimation