NDLI: Regularized Robust Estimation of Mean and Covariance Matrix Under Heavy-Tailed Distributions

Content Provider	IEEE Xplore Digital Library
Author	Ying Sun Babu, P. Palomar, D.P.
Copyright Year	1991
Abstract	In this paper, the joint mean-covariance estimation problem is considered under the scenario that the number of samples is small relative to the problem dimension. The samples are assumed drawn independently from a heavy-tailed distribution of the elliptical family, which can model scenarios where the commonly adopted Gaussian assumption is violated either because of the data generating process or the contamination of outliers. Under the assumption that prior knowledge of the mean and covariance matrix is available, we propose a regularized estimator defined as the minimizer of a penalized loss function, which combines the prior information and the information provided by the samples. The loss function is chosen to be the negative log-likelihood function of the Cauchy distribution as a conservative representative of heavy-tailed distributions, and the penalty term is constructed with the prior being its global minimizer. The resulting regularized estimator shrinks the mean and the covariance matrix to the prior target. The existence and uniqueness of the estimator for finite samples are established under certain regularity conditions. Numerical algorithms are derived for the estimator based on the majorization-minimization framework with guaranteed convergence and simulation results demonstrate that the proposed estimator achieves better estimation accuracy compared to the benchmark estimators.
Sponsorship	IEEE Signal Processing Society
Starting Page	3096
Ending Page	3109
Page Count	14
File Size	3624367
File Format	PDF
ISSN	1053587X
Volume Number	63
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Covariance matrices Robustness Maximum likelihood estimation Joints Signal processing algorithms Symmetric matrices robust estimation Iterative shrinkage majorization-minimization regularization
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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