Related papers: Random matrix theory and robust covariance matrix …
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…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…
This paper studies the spectral behavior of large dimensional Chatterjee's rank correlation matrix when observations are independent draws from a high-dimensional random vector with independent continuous components. We show that the…
We study the problem of computationally efficient robust estimation of the covariance/scatter matrix of elliptical distributions -- that is, affine transformations of spherically symmetric distributions -- under the strong contamination…
The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each…
Multivariate statistical analysis is concerned with observations on several variables which are thought to possess some degree of inter-dependence. Driven by problems in genetics and the social sciences, it first flowered in the earlier…
For a sample of $n$ independent identically distributed $p$-dimensional centered random vectors with covariance matrix $\mathbf{\Sigma}_n$ let $\tilde{\mathbf{S}}_n$ denote the usual sample covariance (centered by the mean) and…
We review the random matrix theory describing elastic scattering through zero-dimensional ballistic cavities (having chaotic classical dynamics) and quasi-one dimensional disordered systems. In zero dimension, general symmetry…
We derive the universality principle for empirical spectral distributions of sample covariance matrices and their Stieltjes transforms. This principle states the following. Suppose quadratic forms of random vectors $y_p$ in $R^p$ satisfy a…
A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic…
This survey provides a self-contained account of $M$-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying $M$-functionals and discuss their weak continuity and differentiability. This is…
We prove that Kendall's Rank correlation matrix converges to the Mar\v{c}enko-Pastur law, under the assumption that the observations are i.i.d random vectors $X_1$, $\dots$, $X_n$ with components that are independent and absolutely…
Since it was first applied to the study of nuclear interactions by Wigner and Dyson, almost 60 years ago, Random Matrix Theory (RMT) has developed into a field of its own within applied mathematics, and is now essential to many parts of…
Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov regularization), regularized discriminant…
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free…
For two large matrices ${\mathbf X}$ and ${\mathbf Y}$ with Gaussian i.i.d.\ entries and dimensions $T\times N_X$ and $T\times N_Y$, respectively, we derive the probability distribution of the singular values of $\mathbf{X}^T \mathbf{Y}$ in…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
A central limit theorem (CLT) for the smoothed empirical spectral distribution of sample covariance matrices is established. Moreover, the CLTs for the smoothed quantiles of Marcenko and Pastur's law have been also developed.