Robust Semiparametric Efficient Estimators in Complex Elliptically Symmetric Distributions
| Autor: | Alexandre Renaux, Frédéric Pascal, Stefano Fortunati |
|---|---|
| Přispěvatelé: | Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), ANR-17-ASTR-0015,MARGARITA,Nouvelles Techniques Robustes et d'Inférences pour le Radar Adaptatif Moderne(2017) |
| Rok vydání: | 2020 |
| Předmět: |
[STAT.AP]Statistics [stat]/Applications [stat.AP]
Computer science Estimator 020206 networking & telecommunications Probability density function robust estimation [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] 02 engineering and technology scatter matrix estimation Covariance Semiparametric model Matrix (mathematics) Scatter matrix Robustness (computer science) Signal Processing Outlier 0202 electrical engineering electronic engineering information engineering Semiparametric models Symmetric matrix Applied mathematics el- liptically symmetric distributions Le Cam's one-step estimator Electrical and Electronic Engineering ranks [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing |
| Zdroj: | IEEE Transactions on Signal Processing IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2020, 68, pp.5003-5015. ⟨10.1109/TSP.2020.3019110⟩ |
| ISSN: | 1941-0476 1053-587X |
| DOI: | 10.1109/tsp.2020.3019110 |
| Popis: | International audience; 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 location 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 one-step efficient estimators and the rank-based statistics. In this paper, we firstly recall the building blocks underlying the derivation of such real-valued R-estimator, then its extension to complex-valued data is proposed. Moreover, through numerical simulations, its estimation performance and robustness to outliers are investigated in a finite-sample regime. |
| Databáze: | OpenAIRE |
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