Related papers: Joint CLT for eigenvalue statistics from several d…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
Under a multinormal distribution with an arbitrary unknown covariance matrix, the main purpose of this paper is to propose a framework to achieve the goal of reconciliation of Bayesian, frequentist, and Fisher's reporting $p$-values,…
The classic likelihood ratio test for testing the equality of two covariance matrices breakdowns due to the singularity of the sample covariance matrices when the data dimension $p$ is larger than the sample size $n$. In this paper, we…
The multivariate nonlinear Granger causality developed by Bai et al. (2010) plays an important role in detecting the dynamic interrelationships between two groups of variables. Following the idea of Hiemstra-Jones (HJ) test proposed by…
We introduce a new random matrix model called distance covariance matrix in this paper, whose normalized trace is equivalent to the distance covariance. We first derive a deterministic limit for the eigenvalue distribution of the distance…
The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization with space-time grid for a parabolic diffusion problem and from the approximation of…
We prove the Central Limit Theorem for finite-dimensional vectors of linear eigenvalue statistics of submatrices of Wigner random matrices under the assumption that test functions are sufficiently smooth. We connect the asymptotic…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…
A fundamental concept in multivariate statistics, sample correlation matrix, is often used to infer the correlation/dependence structure among random variables, when the population mean and covariance are unknown. A natural block extension…
We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…
We investigate the statistical properties of the eigenvalues and eigenvectors in a random matrix ensemble with $H_{ij}\sim |i-j|^{-\mu}$. It is known that this model shows a localization-delocalization transition (LDT) as a function of the…
This paper investigates the asymptotic properties of quantile regression estimators in linear models, with a particular focus on polynomial regressors and robustness to heavy-tailed noise. Under independent and identically distributed…
We introduce a new ``$(m,mp/n)$ out of $(n,p)$'' sampling-with-replace\-ment bootstrap for eigenvalue statistics of high-dimensional sample covariance matrices based on $n$ independent $p$-dimensional random vectors. As it only uses…
We consider $N$ by $N$ deformed Wigner random matrices of the form $X_N=H_N+A_N$, where $H_N$ is a real symmetric or complex Hermitian Wigner matrix and $A_N$ is a deterministic real bounded diagonal matrix. We prove a universal Central…
Statistics derived from the eigenvalues of sample covariance matrices are called spectral statistics, and they play a central role in multivariate testing. Although bootstrap methods are an established approach to approximating the laws of…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…
Determining the number of common factors is an important and practical topic in high dimensional factor models. The existing literatures are mainly based on the eigenvalues of the covariance matrix. Due to the incomparability of the…
In this work, we are motivated by the recent work of Zhang et al. (2019) and study a new invariant test for equality of two large scale covariance matrices. Two modified likelihood ratio tests (LRTs) by Zhang et al. (2019) are based on the…
In many medical and biological investigations, including genetics, it is typical to handle high dimensional data which can be viewed as a set of values of some factors and a binary response variable. For instance, the response variable can…