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Titlebook: Elliptically Symmetric Distributions in Signal Processing and Machine Learning; Jean-Pierre Delmas,Mohammed Nabil El Korso,Frédéri Book 20

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Background on Real and Complex Elliptically Symmetric Distributions,tions are provided with their main properties. Finally, the estimation of the symmetry center and scatter matrix is briefly discussed through the sample mean (SM), sample covariance matrix (SCM) estimate, maximum estimate (ML), .-estimators, and Tyler’s .-estimators. Particular attention will be pai
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Robust Estimation with Missing Values for Elliptical Distributions the proposed algorithms are designed to handle various patterns of missing values. At the end of the chapter, the performances of the proposed procedures are illustrated on simulated datasets with missing values. We share a link to a code repository for fully reproducible experiments.
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Semiparametric Estimation in Elliptical Distributionsinfinite-dimensional nuisance term. In particular, the three building blocks of the semiparametric theory, that are ., . and ., will be introduced. By means of these abstract concepts, we define the semiparametric counterpart of the Fisher Information Matrix (FIM) and the related semiparametric effi
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Performance Analysis of Subspace-Based Algorithms in CES Data Modelsnce matrix (SSCM). The asymptotic distributions of these estimators are also derived. This enables us to unify the asymptotic distribution of subspace projectors adapted to the different models of the data and demonstrate various invariance properties that have impacts on the parameters to be estima
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