Properties of a new $R$-estimator of shape matrices
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 real-valued case and then extended to the complex field in our recent work, this $R$-estimator has the remarkable property to be, at the same time, \textit{distributionally robust} and \textit{semiparametric efficient}. Here, the efficiency of different possible configurations of this $R$-estimator are investigated by comparing the resulting Mean Square Error (MSE) with the Constrained Semiparametric Cram\'{e}r-Rao Bound (CSCRB). Moreover, its robustness to outliers is assessed and compared with the one of the celebrated Tyler's estimator.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Estimation of Monge Matrices
Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for a…
Covariance Descriptors for 3D Shape Matching and Retrieval
Several descriptors have been proposed in the past for 3D shape analysis, yet none of them achieves best performance on all shape classes. In this paper we propose a novel method for 3D shape analysis using the covarianc…
ClusteringRetrievalOptimal Rates of Statistical Seriation
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where…
DenoisingMultifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices
We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices. The estimator is positive definite by construction…
Metric LearningregressionIntrinsic Riemannian Cross-covariance for Manifold-valued Random Objects
Covariance estimation yields a fundamental second-order statistic underlying representation learning, dimension reduction, and dependence modeling. While covariance has been well understood in Euclidean spaces, it is ill…
Representation Learning