4,551 research outputs found
Spatial Sign Correlation
A new robust correlation estimator based on the spatial sign covariance
matrix (SSCM) is proposed. We derive its asymptotic distribution and influence
function at elliptical distributions. Finite sample and robustness properties
are studied and compared to other robust correlation estimators by means of
numerical simulations.Comment: 20 pages, 7 figures, 2 table
Covariance Estimation in Elliptical Models with Convex Structure
We address structured covariance estimation in Elliptical distribution. We
assume it is a priori known that the covariance belongs to a given convex set,
e.g., the set of Toeplitz or banded matrices. We consider the General Method of
Moments (GMM) optimization subject to these convex constraints. Unfortunately,
GMM is still non-convex due to objective. Instead, we propose COCA - a convex
relaxation which can be efficiently solved. We prove that the relaxation is
tight in the unconstrained case for a finite number of samples, and in the
constrained case asymptotically. We then illustrate the advantages of COCA in
synthetic simulations with structured Compound Gaussian distributions. In these
examples, COCA outperforms competing methods as Tyler's estimate and its
projection onto a convex set
Tyler's Covariance Matrix Estimator in Elliptical Models with Convex Structure
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
Moments (GMM) optimization applied to robust Tyler's scatter M-estimator
subject to these convex constraints. Unfortunately, GMM turns out to be
non-convex due to the objective. Instead, we propose a new COCA estimator - a
convex relaxation which can be efficiently solved. We prove that the relaxation
is tight in the unconstrained case for a finite number of samples, and in the
constrained case asymptotically. We then illustrate the advantages of COCA in
synthetic simulations with structured compound Gaussian distributions. In these
examples, COCA outperforms competing methods such as Tyler's estimator and its
projection onto the structure set.Comment: arXiv admin note: text overlap with arXiv:1311.059
A cautionary note on robust covariance plug-in methods
Many multivariate statistical methods rely heavily on the sample covariance
matrix. It is well known though that the sample covariance matrix is highly
non-robust. One popular alternative approach for "robustifying" the
multivariate method is to simply replace the role of the covariance matrix with
some robust scatter matrix. The aim of this paper is to point out that in some
situations certain properties of the covariance matrix are needed for the
corresponding robust "plug-in" method to be a valid approach, and that not all
scatter matrices necessarily possess these important properties. In particular,
the following three multivariate methods are discussed in this paper:
independent components analysis, observational regression and graphical
modeling. For each case, it is shown that using a symmetrized robust scatter
matrix in place of the covariance matrix results in a proper robust
multivariate method.Comment: 24 pages, 7 figure
Asymptotic properties of robust complex covariance matrix estimates
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 on covariance matrix estimation problems in non-Gaussian
environments and particularly, the M-estimators in the context of elliptical
distributions. Firstly, this paper extends to the complex case the results of
Tyler in [1]. More precisely, the asymptotic distribution of these estimators
as well as the asymptotic distribution of any homogeneous function of degree 0
of the M-estimates are derived. On the other hand, we show the improvement of
such results on two applications: DOA (directions of arrival) estimation using
the MUSIC (MUltiple SIgnal Classification) algorithm and adaptive radar
detection based on the ANMF (Adaptive Normalized Matched Filter) test
Asymptotics of the two-stage spatial sign correlation
Acknowledgments This research was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. The authors wish to thank the editors and referees for their careful handling of the manuscript. They further acknowledge the anonymous referees of the article Spatial sign correlation (J. Multivariate Anal. 135, pages 89–105, 2015), who independently of each other suggested to further explore the properties of two-stage spatial sign correlation.Non peer reviewedPreprin
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