Related papers: On eigenvalues of a high-dimensional Kendall's ran…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
In this paper, we investigate the limiting spectral distribution of the sample correlation matrix, whose sample vectors are $k$-fold tensor products of $n$-dimensional vectors with i.i.d. entries. We focus on the limiting regime $n,k \to…
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…
Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely…
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 study the eigenvalue distributions for sums of independent rank-one $k$-fold tensor products of large $n$-dimensional vectors. Previous results in the literature assume that $k=o(n)$ and show that the eigenvalue distributions converge to…
This paper introduces a new method to estimate the spectral distribution of a population covariance matrix from high-dimensional data. The method is founded on a meaningful generalization of the seminal Marcenko-Pastur equation, originally…
Consider a $p$-dimensional population ${\mathbf x} \in\mathbb{R}^p$ with iid coordinates in the domain of attraction of a stable distribution with index $\alpha\in (0,2)$. Since the variance of ${\mathbf x}$ is infinite, the sample…
We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…
The multivariate Kendall-$\tau$ statistic, denoted by $K_n$, plays a significant role in robust statistical analysis. This paper establishes the limiting properties of the empirical spectral distribution (ESD) of $K_n$. We demonstrate that…
This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among…
We study the limiting spectral distribution of large-dimensional sample covariance matrices associated with symmetric random tensors formed by $\binom{n}{d}$ different products of $d$ variables chosen from $n$ independent standardized…
In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the…
We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…
In this paper, we investigate the limiting empirical spectral distribution (LSD) of sums of independent rank-one $k$-fold tensor products of $n$-dimensional vectors as $k,n \to \infty$. Assuming that the base vectors are complex random…
We consider a class of real random matrices with dependent entries and show that the limiting empirical spectral distribution is given by the Marchenko-Pastur law. Additionally, we establish a rate of convergence of the expected empirical…
In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…
In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects.…
This paper is concerned with Spearman's correlation matrices under large dimensional regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear…
We study an "inner-product kernel" random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large $n$ and $p$ limit. We provide an interpretation of…