Related papers: Signal and Noise in Correlation Matrix
Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
We analyse the structure of the distribution of eigenvalues of the stock market correlation matrix with increasing length of the time series representing the price changes. We use 100 highly-capitalized stocks from the American market and…
We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occuring repeatedly at consecutive time-intervals. As an application we analyse the magnetoencephalography recordings obtained from…
The exact meaning of the noise spectrum of eigenvalues of the covariance matrix is discussed. In order to better understand the possible phenomena behind the observed noise, the spectrum of eigenvalues of the covariance matrix is studied…
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…
For a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions. Recent advances show that the scope of random matrix theory is much wider. In this work, we show…
Covariance matrix estimation concerns the problem of estimating the covariance matrix from a collection of samples, which is of extreme importance in many applications. Classical results have shown that $O(n)$ samples are sufficient to…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
We discuss a practical method to determine the eigenvalue spectrum of the empirical correlation matrix. The method is based on the analysis of the behavior of a conformal map at a critical horizon which is defined as a border line of the…
We summarize properties of the spatial sign covariance matrix and especially look at the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…
Estimation of the covariance matrix of asset returns is crucial to portfolio construction. As suggested by economic theories, the correlation structure among assets differs between emerging markets and developed countries. It is therefore…
Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a linear latent feature model with additive noise constructed from probabilistic…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…