Robust Statistics for Signal Processing

Zoubir, Abdelhak M.; Koivunen, Visa; Ollila, Esa; Muma, Michael

doi:10.1017/9781139084291

Cited by 160 publications

(146 citation statements)

References 234 publications

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“…Definition II.1. ( [9], [10], [12] and [14,Ch. 4]) Let z x R + jx I ∈ C N be a complex random vector and let x R ∈ R N and x I ∈ R N be two real random vectors that represent the real and the imaginary part of z, respectively.…”

Section: A Brief Recap On Ces Distributionsmentioning

confidence: 99%

“…As showed in [18, Theo. IV.1] for the real case, the first step to obtain CCSCRB(φ 0 |h 0 ) is the derivation of the matrix U whose columns form an orthonormal basis for the null space of the Jacobian matrix of the constraint function c(Σ 0 ) in (14). Since, in our case, c(Σ 0 ) involves only the real diagonal elements of the Hermitian matrix Σ 0 , U ∈ R N 2 ×(N 2 −1) is the matrix that satisfies the following two conditions:…”

Section: Distributionsmentioning

confidence: 99%

“…This fact, together with the need to model the non-Gaussian, heavy-tailed statistical behavior of the disturbance, led to the introduction of the wide family of Complex Elliptical Symmetric (CES) distributions ( [9], [10,Ch. 3], [11], [12], [13] and [14,Ch. 4]).…”

Section: Introductionmentioning

confidence: 99%

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Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions

Fortunati

Gini

Greco

et al. 2019

IEEE Trans. Signal Process.

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The main aim of this paper is to extend the semiparametric inference methodology, recently investigated for Real Elliptically Symmetric (RES) distributions, to Complex Elliptically Symmetric (CES) distributions. The generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data. Moreover, the CES distributions has been widely recognized as a valuable and general model to statistically describe the non-Gaussian behaviour of datasets originated from a wide variety of physical measurement processes. The paper is divided in two parts. In the first part, a closed form expression of the constrained Semiparametric Cramér-Rao Bound (CSCRB) for the joint estimation of complex mean vector and complex scatter matrix of a set of CES-distributed random vectors is obtained by exploiting the so-called Wirtinger or CR-calculus.The second part deals with the derivation of the semiparametric version of the Slepian-Bangs formula in the context of the CES model. Specifically, the proposed Semiparametric Slepian-Bangs (SSB) formula provides us with a useful and ready-to-use expression of the Semiparametric Fisher Information Matrix (SFIM) for the estimation of a parameter vector parametrizing the complex mean and the complex scatter S. Fortunati is with

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Section: A Brief Recap On Ces Distributionsmentioning

confidence: 99%

Section: Distributionsmentioning

confidence: 99%

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Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions

Fortunati

Gini

Greco

et al. 2019

IEEE Trans. Signal Process.

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“…The weight function ϕ(t) for Tyler's estimator is defined as (see e.g. [14,43] and [15,Ch. 4] and references therein):…”

Section: π(L|tmentioning

confidence: 99%

“…As we will discuss below, a constraint on Sigma is required to avoid the scale ambiguity that characterizes the definition of scatter matrix in RES distributions. The RES class represents a wide family of distributions that includes the Gaussian, the t, the Generalized Gaussian and all the real Compound-Gaussian distributions as special cases ([8]- [14], and [15,Ch. 4]).…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions

Fortunati

Gini

Greco

et al. 2019

IEEE Trans. Signal Process.

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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 semiparametric lower bound for the estimation of the parametric component of the model. The RES distributions represent a semiparametric model where the parametric part is given by the mean vector and by the scatter matrix while the non-parametric, infinite-dimensional, part is represented by the density generator. Since, in practical applications, we are often interested only in the estimation of the parametric component, the density generator can be considered as nuisance.The first part of the paper is dedicated to conveniently place the RES distributions in the framework of the semiparametric group models. The second part of the paper, building on the mathematical tools previously introduced, the Constrained Semiparametric Cramér-Rao Bound (CSCRB) for the estimation of the mean vector and of the constrained scatter matrix of a RES distributed random vector is introduced.The CSCRB provides a lower bound on the Mean Squared Error (MSE) of any robust M -estimator of mean vector and scatter matrix when no a-priori information on the density generator is available.A closed form expression for the CSCRB is derived. Finally, in simulations, we assess the statistical efficiency of the Tyler's and Huber's scatter matrix M -estimators with respect to the CSCRB. S. Fortunati is with

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An Overview of Covariance‐based Change Detection Methodologies in Multivariate SAR Image Time Series

Mian

Ginolhac

Ovarlez

et al. 2021

Change Detection and Image Time Series Analysis 1

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Robust Statistics for Signal Processing

Cited by 160 publications

References 234 publications

Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions

Semiparametric CRB and Slepian-Bangs Formulas for Complex Elliptically Symmetric Distributions

Semiparametric Inference and Lower Bounds for Real Elliptically Symmetric Distributions

An Overview of Covariance‐based Change Detection Methodologies in Multivariate SAR Image Time Series

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