Related papers: Spectral analysis of high-dimensional sample covar…

This article studies the limiting behavior of a class of robust population covariance matrix estimators, originally due to Maronna in 1976, in the regime where both the number of available samples and the population size grow large. Using…

We investigate the asymptotics of eigenvalues of sample covariance matrices associated with a class of non-independent Gaussian processes (separable and temporally stationary) under the Kolmogorov asymptotic regime. The limiting spectral…

We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random…

We analyze the spectral properties of the high-dimensional random geometric graph $G(n, d, p)$, formed by sampling $n$ i.i.d vectors $\{v_i\}_{i=1}^{n}$ uniformly on a $d$-dimensional unit sphere and connecting each pair $\{i,j\}$ whenever…

We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random…

Bandeira et al. (2017) show that the eigenvalues of the Kendall correlation matrix of $n$ i.i.d. random vectors in $\mathbb{R}^p$ are asymptotically distributed like $1/3 + (2/3)Y_q$, where $Y_q$ has a Mar\v{c}enko-Pastur law with parameter…

In this note we develop an extension of the Mar\v{c}enko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for…

We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…

Suppose $\mathbf Y_n=(\mathbf y_1,\cdots,\mathbf y_n)$ is a $p\times n$ data matrix whose columns $\mathbf y_j, 1\leq j\leq n$ have different correlations. The asymptotic spectral property of $\mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n$…

We consider the estimation of integrated covariance (ICV) matrices of high dimensional diffusion processes based on high frequency observations. We start by studying the most commonly used estimator, the realized covariance (RCV) matrix. We…

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…

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…

We consider sparse sample covariance matrices $\frac1{np_n}\mathbf X\mathbf X^*$, where $\mathbf X$ is a sparse matrix of order $n\times m$ with the sparse probability $p_n$. We prove the local Marchenko--Pastur law in some complex domain…

This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples $n$ and their dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with $0<y<1$. We prove…

In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent copies of a stationary regular sequence has a limiting distribution depending only on the spectral density of the…

For a class of symmetric random matrices whose entries are martingale differences adapted to an increasing filtration, we prove that under a Lindeberg-like condition, the empirical spectral distribution behaves asymptotically similarly to a…

We study the asymptotic behavior of the spectra of matrices of the form $S_n = \frac{1}{n}XX^*$ where $X =\sum_{r=1}^K X_r$, where $X_r = A_r^\frac{1}{2}Z_rB_r^\frac{1}{2}$, $K \in \mathbb{N}$ and $A_r,B_r$ are sequences of positive…

We study a model where one target variable Y is correlated with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y. We describe a method that infers to what extent the statistical dependences between X and Y are…

Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…

In this paper, we consider the problem of determining the presence of a given signal in a high-dimensional observation with unknown covariance matrix by using an adaptive matched filter. Traditionally such filters are formed from the sample…