相关论文: A CLT for regularized sample covariance matrices
We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of "homogenization" for Dyson Brownian Motion, this yields the universality of quantities which depend on…
We consider the fluctuation of linear eigenvalue statistics of random band $n\times n$ matrices whose entries have the form $\mathcal{M}_{ij}=b^{-1/2}u^{1/2}(|i-j|)\tilde w_{ij}$ with i.i.d. $w_{ij}$ possessing the $(4+\varepsilon)$th…
In this note, we establish an asymptotic expansion for the centering parameter appearing in the central limit theorems for linear spectral statistic of large-dimensional sample covariance matrices when the population has a spiked covariance…
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…
For $k,m,n\in \mathbb{N}$, we consider $n^k\times n^k$ random matrices of the form $$ \mathcal{M}_{n,m,k}(\mathbf{y})=\sum_{\alpha=1}^m\tau_\alpha {Y_\alpha}Y_\alpha^T,\quad…
We establish a strong law of large numbers and a central limit theorem in the Bures-Wasserstein space of covariance operators -- or equivalently centred Gaussian measures -- over a general separable Hilbert space. Specifically, we show that…
We prove a law of large numbers for empirical approximations of the spectrum of a kernel integral operator by the spectrum of random matrices based on a sample drawn from a Markov chain, which complements the results by V. Koltchinskii and…
This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…
We study the behavior of infinite systems of coupled harmonic oscillators as t->infinity, and generalize the Central Limit Theorem (CLT) to show that their reduced Wigner distributions become Gaussian under quite general conditions. This…
We prove central limit theorem for linear eigenvalue statistics of orthogonally invariant ensembles of random matrices with one interval limiting spectrum. We consider ensembles with real analytic potentials and test functions with two…
This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…
We extend the spectral method for proving limit theorems to random non-uniformly expanding dynamical systems. This yields the CLT and moderate deviations principles (MDP). We show that as the amount of non-uniformity decreases the CLT rates…
Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations,…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
Consider a random vector $\mathbf{y}=\mathbf{\Sigma}^{1/2}\mathbf{x}$, where the $p$ elements of the vector $\mathbf{x}$ are i.i.d. real-valued random variables with zero mean and finite fourth moment, and $\mathbf{\Sigma}^{1/2}$ is a…
We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…
In this article we formulate the CLT associated to Gaussian operators of type B -- see \cite{BEH15}, where important role is played by colored pair partitions. Then we present a certain family of noncommutative random matrix models for the…
We prove the Central Limit Theorem for the number of eigenvalues near the spectrum edge for hermitian ensembles of random matrices. To derive our results, we use a general theorem, essentially due to Costin and Lebowitz, concerning the…
We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…
Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…