Ratio-consistent estimation for long range dependent Toeplitz covariance with application to matrix data whitening

Robust Covariance Matrix Estimation with Data-Dependent VAR Prewhitening Order

Masked Toeplitz covariance estimation

The problem of estimating the covariance matrix Σ of a p-variate distribution based on its n observations arises in many data analysis contexts. While for n > p, the classical sample covariance matrix Σ̂n is a good estimator for Σ, it fails in the highdimensional setting when n ≪ p. In this scenario one requires prior knowledge about the structure of the covariance matrix in order to construct r...

Spatial Heteroskedasticity and Autocorrelation Consistent Estimation of Covariance Matrix

This paper considers spatial heteroskedasticity and autocorrelation consistent (spatial HAC) estimation of covariance matrices of parameter estimators. We generalize the spatial HAC estimators introduced by Kelejian and Prucha (2007) to apply to linear and nonlinear spatial models with moment conditions. We establish its consistency, rate of convergence and asymptotic truncated mean squared err...

Embedding nonnegative definite Toeplitz matrices in nonnegative definite circulant matrices, with application to covariance estimation

Ahtract -The class of nonnegative definite Toeplitz matrices that can be embedded in nonnegative definite circulant matrices of larger sue is characterized. An equivalent characterization in terms of the spectrum of the underlying process is also presented, together with the corresponding extrema1 processes. It is shown that a given finite duration sequence p can be extended to be the covarianc...

Joint mean and covariance estimation with unreplicated matrix - variate data ∗

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrixvariate approaches that impose various forms of (inverse) covariance sparsity allow flexib...