TY - GEN
T1 - Robust shrinkage estimation of high-dimensional covariance matrices
AU - Chen, Yilun
AU - Wiesel, Ami
AU - Hero, Alfred O.
PY - 2010
Y1 - 2010
N2 - We address high dimensional covariance estimation for elliptical distributed samples. 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 iteration. We derive the minimum mean-squared-error shrinkage coefficient in closed form. The closed form expression is a function of the unknown true covariance and cannot be implemented in practice. Instead, we propose a plug-in estimate to approximate it. Simulations demonstrate that the proposed method achieves low estimation error and is robust to heavy-tailed samples.
AB - We address high dimensional covariance estimation for elliptical distributed samples. 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 iteration. We derive the minimum mean-squared-error shrinkage coefficient in closed form. The closed form expression is a function of the unknown true covariance and cannot be implemented in practice. Instead, we propose a plug-in estimate to approximate it. Simulations demonstrate that the proposed method achieves low estimation error and is robust to heavy-tailed samples.
UR - http://www.scopus.com/inward/record.url?scp=78650161161&partnerID=8YFLogxK
U2 - 10.1109/SAM.2010.5606730
DO - 10.1109/SAM.2010.5606730
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AN - SCOPUS:78650161161
SN - 9781424489770
T3 - 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010
SP - 189
EP - 192
BT - 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010
T2 - 2010 IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2010
Y2 - 4 October 2010 through 7 October 2010
ER -