相关论文: Properties of a new $R$-estimator of shape matrice…

The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints.…

Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the \textit{semiparametric} covariance/scatter matrix estimation problem in elliptical distributions. The class…

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…

A class of R-estimators based on the concepts of multivariate signed ranks and the optimal rank-based tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006)] is proposed for the estimation of the shape matrix of an elliptical…

This letter aims at extending the Constrained Semiparametric Cramer-Rao Bound (CSCRB) for the joint estimation of mean vector and scatter matrix of Real Elliptically Symmetric (RES) distributions to Complex Elliptically Symmetric (CES)…

This paper has a twofold goal. The first aim is to provide a deeper understanding of the family of the Real Elliptically Symmetric (RES) distributions by investigating their intrinsic semiparametric nature. The second aim is to derive a…

Estimating the shape of an elliptical distribution is a fundamental problem in statistics. One estimator for the shape matrix, Tyler's M-estimator, has been shown to have many appealing asymptotic properties. It performs well in numerical…

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…

Principal component analysis (PCA) is one of the most popular dimension reduction methods. The usual PCA is known to be sensitive to the presence of outliers, and thus many robust PCA methods have been developed. Among them, the Tyler's…

We combine Tyler's robust estimator of the dispersion matrix with nonlinear shrinkage. This approach delivers a simple and fast estimator of the dispersion matrix in elliptical models that is robust against both heavy tails and high…

This letter aims at deriving a Semiparametric Slepian-Bangs (SSB) formula for Complex Elliptically Symmetric (CES) distributed data vectors. The Semiparametric Cram\'{e}r-Rao Bound (SCRB), related to the proposed SSB formula, provides a…

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…

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on…

This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…

In many problems from multivariate analysis, the parameter of interest is a shape matrix, that is, a normalized version of the corresponding scatter or dispersion matrix. In this paper, we propose a depth concept for shape matrices that…

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…

We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the…

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…

This paper aims at presenting a numerical investigation of the statistical efficiency of the MUSIC (with different covariance matrix estimates) and the IAA-APES Direction of Arrivals (DOAs) estimation algorithms under a general Complex…

This chapter presents a short overview of real elliptically symmetric (RES) distributions, complemented by circular complex elliptically symmetric (C-CES) and noncircular CES (NC-CES) distributions as complex representations of RES…