A high?dimensional classification rule using sample covariance matrix equipped with adjusted estimated eigenvalues

Eigenvalues of the sample covariance matrix for a towed array.

It is well known that observations of the spatial sample covariance matrix (SCM, also called the cross-spectral matrix) reveal that the ordered noise eigenvalues of the SCM decay steadily, but common models predict equal noise eigenvalues. Random matrix theory (RMT) is used to derive and discuss properties of the eigenvalue spectrum of the data SCM for linear arrays, with an application to ocea...

Largest eigenvalues and sample covariance matrices

A Corrector for the Sample Mahalanobis Distance Free from Estimating the Population Eigenvalues of Covariance Matrix

The Eigenvalues of the Sample Covariance Matrix of a Multivariate Heavy-tailed Stochastic Volatility Model

We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for the ordered eigenvalues and corresponding eigenvectors. Essentially, we consider two different cases where the tail behavior either stems from the iid innovati...

Extreme Eigenvalues of Sample Covariance and Correlation Matrices

This thesis is concerned with asymptotic properties of the eigenvalues of high-dimensional sample covariance and correlation matrices under an infinite fourth moment of the entries. In the first part, we study the joint distributional convergence of the largest eigenvalues of the sample covariance matrix of a p-dimensional heavy-tailed time series when p converges to infinity together with the ...