By Topic

Robust Shrinkage Estimation of High-Dimensional Covariance Matrices

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Yilun Chen ; Dept. of Electr. Eng. & Comput. Sci., Univ. of Michigan, Ann Arbor, MI, USA ; Wiesel, A. ; Hero, A.O.

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are suitable for high dimensional problems with a small number of samples (large p small n). We start from a classical robust covariance estimator [Tyler (1987)], which is distribution-free within the family of elliptical distribution but inapplicable when n <; p. Using a shrinkage coefficient, we regularize Tyler's fixed-point iterations. We prove that, for all n and p , the proposed fixed-point iterations converge to a unique limit regardless of the initial condition. Next, we propose a simple, closed-form and data dependent choice for the shrinkage coefficient, which is based on a minimum mean squared error framework. Simulations demonstrate that the proposed method achieves low estimation error and is robust to heavy-tailed samples. Finally, as a real-world application we demonstrate the performance of the proposed technique in the context of activity/intrusion detection using a wireless sensor network.

Published in:

Signal Processing, IEEE Transactions on  (Volume:59 ,  Issue: 9 )