Related papers: Joint convergence of sample cross-covariance matri…

We consider the asymptotic behavior as $n\to\infty$ of the spectra of random matrices of the form \[\frac{1}{\sqrt{n-1}}\sum_{k=1}^{n-1}Z_{nk}\rho_n ((k,k+1)),\] where for each $n$ the random variables $Z_{nk}$ are i.i.d. standard Gaussian…

Given $n,m\in \mathbb{N}$, we study two classes of large random matrices of the form $$ \mathcal{L}_n =\sum_{\alpha=1}^m\xi_\alpha \mathbf{y}_\alpha \mathbf{y}_\alpha ^T\quad\text{and}\quad \mathcal{A}_n =\sum_{\alpha =1}^m\xi_\alpha…

Let $S=XX^T$ be the (unscaled) sample covariance matrix where $X$ is a real $p \times n$ matrix with independent entries. It is well known that if the entries of $X$ are independent and identically distributed (i.i.d.) with enough moments…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

Consider a random $n\times n$ zero-one matrix with "density" $p$, sampled according to one of the following two models: either every entry is independently taken to be one with probability $p$ (the "Bernoulli" model), or each row is…

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…

We study the limiting spectral distribution of sample covariance matrices $XX^T$, where $X$ are $p\times n$ random matrices with correlated entries, for the cases $p/n\to y\in [0,\infty)$. If $y>0$, we obtain the Mar\v{c}enko-Pastur…

It is known (Hofmann-Credner and Stolz (2008)) that the convergence of the mean empirical spectral distribution of a sample covariance matrix W_n = 1/n Y_n Y_n^t to the Mar\v{c}enko-Pastur law remains unaffected if the rows and columns of…

Let $\mathbf{X}_p=(\mathbf{s}_1,...,\mathbf{s}_n)=(X_{ij})_{p \times n}$ where $X_{ij}$'s are independent and identically distributed (i.i.d.) random variables with $EX_{11}=0,EX_{11}^2=1$ and $EX_{11}^4<\infty$. It is showed that the…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

This paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form $\mathbf S_n=\frac1n\mathbf B_n\mathbf X_n\mathbf X_n^*\mathbf B_n^*$, where…

Suppose that A_1,\dots, A_N are independent random matrices whose atoms are iid copies of a random variable \xi of mean zero and variance one. It is known from the works of Newman et. al. in the late 80s that when \xi is gaussian then…

It is established that the linear spectral statistics (LSS) of the smoothed periodogram estimate of the spectral coherence matrix of a complex Gaussian high-dimensional times series (yn) n$\in$Z with independent components satisfy at each…

Let the dimension $N$ of data and the sample size $T$ tend to $\infty$ with $N/T \to c > 0$. The spectral properties of a sample correlation matrix $\mathbf{C}$ and a sample covariance matrix $\mathbf{S}$ are asymptotically equal whenever…

We derive the Marchenko-Pastur (MP) law for sample covariance matrices of the form $V_n=\frac{1}{n}XX^T$, where $X$ is a $p\times n$ data matrix and $p/n\to y\in(0,\infty)$ as $n,p \to \infty$. We assume the data in $X$ stems from a…

We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density,…

This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral…

Let $\mathbf{R}$ be the sample correlation matrix constructed from $\mathbf{X}\in \mathbb{R}^{p\times n}$, whose entries are independent and identically distributed random variables with mean zero and tail probability condition…

Suppose that $\mathbf X_n=(x_{jk})$ is $N\times n$ whose elements are independent real variables with mean zero, variance 1 and the fourth moment equal to three. The separable sample covariance matrix is defined as $\mathbf{B}_n =…

Let $\mathbf{a}_{ij}$, $1\leq i\leq j\leq n$, be independent random variables and $\mathbf{a}_{ji}=\mathbf{a}_{ij}$, for all $i,j$. Suppose that every $\mathbf{a}_{ij}$ is bounded, has zero mean, and its variance is given by…