Related papers: Large Dimensional Analysis and Optimization of Rob…
There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…
Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework…
We address structured covariance estimation in elliptical distributions by assuming that the covariance is a priori known to belong to a given convex set, e.g., the set of Toeplitz or banded matrices. We consider the General Method of…
We elucidate the problem of estimating large-dimensional covariance matrices in the presence of correlations between samples. To this end, we generalize the Marcenko-Pastur equation and the Ledoit-Peche shrinkage estimator using methods of…
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…
We address the problem of robust sparse estimation of the precision matrix for heavy-tailed distributions in high-dimensional settings. In such high-dimensional contexts, we observe that the covariance matrix can be approximated by a…
This paper aims at presenting a simulative analysis of the main properties of a new $R$-estimator of shape matrices in Complex Elliptically Symmetric (CES) distributed observations. First proposed by Hallin, Oja and Paindaveine for the…
Elliptically symmetric distributions are widely used in portfolio modeling, as well as in signal processing applications for modeling impulsive background noises. Of particular interest are algorithms for covariance estimation and subspace…
We propose a new class of robust and Fisher-consistent estimators for mixture models. These estimators can be used to construct robust model-based clustering procedures. We study in detail the case of multivariate normal mixtures and…
In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these applications deal with complex data. This paper focuses…
Analyzing large samples of high-dimensional data under dependence is a challenging statistical problem as long time series may have change points, most importantly in the mean and the marginal covariances, for which one needs valid tests.…
In this paper, a general class of regularized $M$-estimators of scatter matrix are proposed which are suitable also for low or insufficient sample support (small $n$ and large $p$) problems. The considered class constitutes a natural…
We propose a flexible class of models based on scale mixture of uniform distributions to construct shrinkage priors for covariance matrix estimation. This new class of priors enjoys a number of advantages over the traditional scale mixture…
In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
This paper proposes an original approach to better understanding the behavior of robust scatter matrix $M$-estimators. Scatter matrices are of particular interest for many signal processing applications since the resulting performance…
Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…
This paper investigates regularized estimation of Kronecker-structured covariance matrices (CM) for polarization radar in sea clutter scenarios where the data are assumed to follow the complex, elliptically symmetric (CES) distributions…
In this paper, we study robust covariance estimation under the approximate factor model with observed factors. We propose a novel framework to first estimate the initial joint covariance matrix of the observed data and the factors, and then…
Meta-analyses frequently include trials that report multiple effect sizes based on a common set of study participants. These effect sizes will generally be correlated. Cluster-robust variance-covariance estimators are a fruitful approach…