Related papers: Large deviations for eigenvalues of sample covaria…
In this paper, we study the fluctuation of linear eigenvalue statistics of Random Band Matrices defined by $M_{n}=\frac{1}{\sqrt{b_{n}}}W_{n}$, where $W_{n}$ is a $n\times n$ band Hermitian random matrix of bandwidth $b_{n}$, i.e., the…
We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part,…
Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this…
We compute analytically, for large $N$, the probability $\mathcal{P}(N_+,N)$ that a $N\times N$ Wishart random matrix has $N_+$ eigenvalues exceeding a threshold $N\zeta$, including its large deviation tails. This probability plays a…
For a generalization of Johnstone's spiked model, a covariance matrix with eigenvalues all one but $M$ of them, the number of features $N$ comparable to the number of samples $n: N=N(n), M=M(n), \gamma^{-1} \leq \frac{N}{n} \leq \gamma$…
This short paper reports some initial experimental demonstrations of the theoretical framework: the massive amount of data in the large-scale cognitive radio network can be naturally modeled as (large) random matrices. In particular, using…
This short note studies the fluctuations of the largest eigenvalue of symmetric random matrices with correlated Gaussian entries having positive mean. Under the assumption that the covariance kernel is absolutely summable, it is proved that…
The major sources of abundant data are constantly expanding with the available data collection methodologies in various applications - medical, insurance, scientific, bio-informatics and business. These data sets may be distributed…
In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the…
Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
The largest eigenvalue of a Wishart matrix, known as Roy's largest root (RLR), plays an important role in a variety of applications. Most works to date derived approximations to its distribution under various asymptotic regimes, such as…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
We consider the classical problem of estimating the covariance matrix of a subgaussian distribution from i.i.d. samples in the novel context of coarse quantization, i.e., instead of having full knowledge of the samples, they are quantized…
Given a probability distribution in R^n with general (non-white) covariance, a classical estimator of the covariance matrix is the sample covariance matrix obtained from a sample of N independent points. What is the optimal sample size N =…
We propose a novel pilot structure for covariance matrix estimation in massive multiple-input multiple-output (MIMO) systems in which each user transmits two pilot sequences, with the second pilot sequence multiplied by a random…
In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results is extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a…
We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the…
This paper investigates global and local laws for sample covariance matrices with general growth rates of dimensions. The sample size $N$ and population dimension $M$ can have the same order in logarithm, which implies that their ratio…
In this article we investigate high-dimensional banded sample covariance matrices under the regime that the sample size $n$, the dimension $p$ and the bandwidth $d$ tend simultaneously to infinity such that $$n/p\to 0 \ \ \text{and} \ \…