Regularization for high-dimensional covariance matrix

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...

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 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...

Approaches to High-Dimensional Covariance and Precision Matrix Estimation

Some Tests concerning the Covariance Matrix in High Dimensional Data

In this paper, tests are developed for testing certain hypotheses on the covariance matrix Σ, when the sample size N = n+1 is smaller than the dimension p of the data. Under the condition that (trΣ/p) exists and > 0, as p → ∞, i = 1, . . . , 8, tests are developed for testing the hypotheses that the covariance matrix in a normally distributed data is an identity matrix, a constant time the iden...