Misspecified Cramér-rao bounds for complex unconstrained and constrained parameters

Fortunati, Stefano

doi:10.23919/eusipco.2017.8081488

Cited by 8 publications

(9 citation statements)

References 21 publications

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“…We can always maps a complex parameter vector into a real one simply by stacking its real and the imaginary parts as e.g. in [Ren15] or we could exploit the so-called Wirtinger calculus as discussed in [Ric15] and [For17].…”

Section: Xm Pmentioning

confidence: 99%

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications

Fortunati

Gini

Greco

et al. 2017

IEEE Signal Process. Mag.

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106

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Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the core of a plethora of scientific and technological advances in the last decades; for example, wireless communications, radar and sonar, biomedicine, image processing, and seismology, just to name a few.Developing an estimation algorithm often begins by assuming a statistical model for the measured data, i.e. a probability density function (pdf), which if correct, fully characterizes the behaviour of the collected data/measurements. Experience with real data, however, often exposes the limitations of any assumed data model since modelling errors at some level are always present. Consequently, the true data model and the model assumed to derive the estimation algorithm could differ. When this happens, the model is said to be mismatched or misspecified. Therefore, understanding the possible performance loss or regret that an estimation algorithm could experience under model misspecification is of crucial importance for any SP practitioner. Further, understanding the limits on the performance of any estimator subject to model misspecification is of practical interest.Motivated by the widespread and practical need to assess the performance of a "mismatched" estimator, the goal of this paper is to help to bring attention to the main theoretical

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Section: Xm Pmentioning

confidence: 99%

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications

Fortunati

Gini

Greco

et al. 2017

IEEE Signal Process. Mag.

Self Cite

106

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show abstract

“…However, a number of fundamental issues still remain to be fully addressed. In our opinion, the most important one is related to the estimation of α 0,g in (53). The estimator in (54) in fact is consistent but it does not satify any optimal property.…”

Section: Discussionmentioning

confidence: 92%

“…However, the use of a real representation of complex quantities usually leads to a loss in the clarity and even in the interpretability of the results. Best practice is then to work directly in the complex filed by means of the Wirtinger calculus [48]- [53]. Basically, the Wirtinger calculus generalizes the concept of complex derivative to non-holomorphic, realvalued functions of complex variables.…”

Section: Extension To Complex Es Distributionsmentioning

confidence: 99%

Robust Semiparametric Efficient Estimators in Elliptical Distributions

Fortunati,

Renaux,

Pascal

2020

Preprint

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Covariance matrices play a major role in statistics, signal processing and machine learning applications. This paper focuses on the semiparametric covariance/scatter matrix estimation problem in elliptical distributions. The class of elliptical distributions can be seen as a semiparametric model where the finite-dimensional vector of interest is given by the mean vector and by the (vectorized) covariance/scatter matrix, while the density generator represents an infinite-dimensional nuisance function. The main aim of this work is then to provide possible estimators of the finite-dimensional parameter vector able to reconcile the two dichotomic concepts of robustness and (semiparametric) efficiency. An R-estimator satisfying these requirements has been recently proposed by Hallin, Oja and Paindaveine for real-valued elliptical data by exploiting the Le Cam's theory of Local Asymptotic Normality (LAN) and the rank-based statistics. In this paper, we firstly provide a survey about the building blocks needed to derive such a robust and semiparametric efficient R-estimator, then its extension to complex-valued data is proposed. Finally, through numerical simulations, its estimation performance is investigated in finitesample regime by comparing its Mean Squared Error with the Semiparametric Cramér-Rao Bound in different scenarios.

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“…Firstly, we will provide a closed form expression for the SCRB on the Mean Square Error (MSE) of the joint estimation of the complex mean vector µ and complex scatter matrix Σ of a set of CES distributed random vectors. This generalization relies on the Wirtinger or CR-calculus ([5]- [7,27]- [30]) and on its application on the derivation of lower bounds ( [31]- [36]). Then, the second part of the paper is dedicated to the derivation of a semiparametric version of the the celebrated Slepian-Bangs (SB) formula and the related Semiparametric Stochastic CRB (SSCRB) for Direction of Arrival (DOA) estimation problems.…”

Section: Introductionmentioning

confidence: 99%

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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Misspecified Cramér-rao bounds for complex unconstrained and constrained parameters

Cited by 8 publications

References 21 publications

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications

Performance Bounds for Parameter Estimation under Misspecified Models: Fundamental Findings and Applications

Robust Semiparametric Efficient Estimators in Elliptical Distributions

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

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