8,449 research outputs found
Asymptotic properties of robust complex covariance matrix estimates
In many statistical signal processing applications, the estimation of
nuisance parameters and parameters of interest is strongly linked to the
resulting performance. Generally, these applications deal with complex data.
This paper focuses on covariance matrix estimation problems in non-Gaussian
environments and particularly, the M-estimators in the context of elliptical
distributions. Firstly, this paper extends to the complex case the results of
Tyler in [1]. More precisely, the asymptotic distribution of these estimators
as well as the asymptotic distribution of any homogeneous function of degree 0
of the M-estimates are derived. On the other hand, we show the improvement of
such results on two applications: DOA (directions of arrival) estimation using
the MUSIC (MUltiple SIgnal Classification) algorithm and adaptive radar
detection based on the ANMF (Adaptive Normalized Matched Filter) test
A generalization of Tyler's M-estimators to the case of incomplete data
Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established until today. Tyler's M-estimator has been recognized as the 'most robust' M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler's Mestimators for location and shape are generalized by taking account of incomplete data. It is shown that the shape matrix estimator remains distribution-free under the class of generalized elliptical distributions. Its asymptotic distribution is also derived and a fast algorithm, which works well even for high-dimensional data, is presented. A simulation study with clean and contaminated data covers the complete-data as well as the incomplete-data case, where the missing data are assumed to be MCAR, MAR, and NMAR. --covariance matrix,distribution-free estimation,missing data,robust estimation,shape matrix,sign-based estimator,Tyler's M-estimator
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