Related papers: Regularized $M$-estimators of scatter matrix
Maronna's and Tyler's $M$-estimators are among the most widely used robust estimators for scatter matrices. However, when the dimension of observations is relatively high, their performance can substantially deteriorate in certain…
In this paper, we study properties of penalized and structured M-estimators of multivariate scatter, based on geodesically convex but not necessarily smooth penalty functions. Existence and uniqueness conditions for these penalized and…
In this paper, {we propose an alternative proof for the uniqueness} of Maronna's $M$-estimator of scatter (Maronna, 1976) for $N$ vector observations $\mathbf y_1,...,\mathbf y_N\in\mathbb R^m$ under a mild constraint of linear independence…
This article addresses improvements on the design of the adaptive normalized matched filter (ANMF) for radar detection. It is well-acknowledged that the estimation of the noise-clutter covariance matrix is a fundamental step in adaptive…
This paper considers the regularized Tyler's scatter estimator for elliptical distributions, which has received considerable attention recently. Various types of shrinkage Tyler's estimators have been proposed in the literature and proved…
A common assumption when sampling $p$-dimensional observations from $K$ distinct group is the equality of the covariance matrices. In this paper, we propose two penalized $M$-estimation approaches for the estimation of the covariance or…
As observed by Auderset et al. (2005) and Wiesel (2012), viewing covariance matrices as elements of a Riemannian manifold and using the concept of geodesic convexity provide useful tools for studying M-estimators of multivariate scatter. In…
This article studies the behavior of regularized Tyler estimators (RTEs) of scatter matrices. The key advantages of these estimators are twofold. First, they guarantee by construction a good conditioning of the estimate and second, being a…
We introduce a class of regularized M-estimators of multivariate scatter and show, analogous to the popular spatial sign covariance matrix (SSCM), that they possess high breakdown points. We also show that the SSCM can be viewed as an…
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…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
Estimating a high-dimensional sparse covariance matrix from a limited number of samples is a fundamental problem in contemporary data analysis. Most proposals to date, however, are not robust to outliers or heavy tails. Towards bridging…
This article investigates the asymptotic distribution of penalized estimators with non-differentiable penalties designed to recover low-dimensional pattern structures. Patterns play a central role in estimation, as they reveal the…
This paper studies M-estimators with gradient-Lipschitz loss function regularized with convex penalty in linear models with Gaussian design matrix and arbitrary noise distribution. A practical example is the robust M-estimator constructed…
In this paper, we analyse the recovery properties of nonconvex regularized $M$-estimators, under the assumption that the true parameter is of soft sparsity. In the statistical aspect, we establish the recovery bound for any stationary point…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
Tyler's and Maronna's M-estimators, as well as their regularized variants, are popular robust methods to estimate the scatter or covariance matrix of a multivariate distribution. In this work, we study the non-asymptotic behavior of these…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…