Joint Estimation of Location and Scatter in Complex Elliptical Distributions: A robust semiparametric and computationally efficient R-estimator of the shape matrix

Autor: Alexandre Renaux, Stefano Fortunati, Frédéric Pascal
Přispěvatelé: Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Direction de la Recherche et de l'Innovation de l'IPSA (DRII), Institut Polytechnique des Sciences Avancées (IPSA), ANR-17-ASTR-0015,MARGARITA,Nouvelles Techniques Robustes et d'Inférences pour le Radar Adaptatif Moderne(2017)
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Signal Processing (eess.SP)
FOS: Computer and information sciences
Mean squared error
Computer science
robust estimators
Complex Elliptically Symmetric (CES) distributions
Context (language use)
02 engineering and technology
01 natural sciences
Theoretical Computer Science
Methodology (stat.ME)
Set (abstract data type)
010104 statistics & probability
FOS: Electrical engineering
electronic engineering
information engineering
0202 electrical engineering
electronic engineering
information engineering
Nuisance parameter
Electrical Engineering and Systems Science - Signal Processing
0101 mathematics
Statistics - Methodology
covariance matrix
[STAT.AP]Statistics [stat]/Applications [stat.AP]
Covariance matrix
Estimator
020206 networking & telecommunications
efficient estimators
Hardware and Architecture
Control and Systems Engineering
Modeling and Simulation
Signal Processing
Pattern recognition (psychology)
Semiparametric models
Algorithm
[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Information Systems
Generator (mathematics)
Zdroj: Journal of Signal Processing Systems
Journal of Signal Processing Systems, Springer, 2021, ⟨10.1007/s11265-021-01674-y⟩
ISSN: 1939-8018
1939-8115
DOI: 10.1007/s11265-021-01674-y⟩
Popis: The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints. This joint estimation problem is framed in the original context of semiparametric models allowing us to handle the (generally unknown) density generator as an \textit{infinite-dimensional} nuisance parameter. In the first part of the paper, a computationally efficient and memory saving implementation of the robust and semiparmaetric efficient $R$-estimator for shape matrices is derived. Building upon this result, in the second part, a joint estimator, relying on the Tyler's $M$-estimator of location and on the $R$-estimator of shape matrix, is proposed and its Mean Squared Error (MSE) performance compared with the Semiparametric Cram\'{e}r-Rao Bound (CSCRB).
Comment: This paper has been submitted to the Special Issue (related to MLSP) of the Journal of Signal Processing Systems
Databáze: OpenAIRE
Externí odkaz: