TY - JOUR
T1 - Structured robust covariance estimation
AU - Wiesel, Ami
AU - Zhang, Teng
N1 - Publisher Copyright:
© 2015 A. Wiesel and T. Zhang.
PY - 2014
Y1 - 2014
N2 - We consider robust covariance estimation with an emphasis on Tyler's M-estimator. This method provides accurate inference of an unknown covariance in non-standard settings, including heavy-tailed distributions and outlier contaminated scenarios. We begin with a survey of the estimator and its various derivations in the classical unconstrained settings. The latter rely on the theory of g-convex analysis which we briefly review. Building on this background, we enhance robust covariance estimation via g-convex regularization, and allow accurate inference using a smaller number of samples. We consider shrinkage, diagonal loading, and prior knowledge in the form of symmetry and Kronecker structures. We introduce these concepts to the world of robust covariance estimation, and demonstrate how to exploit them in a computationally and statistically efficient manner.
AB - We consider robust covariance estimation with an emphasis on Tyler's M-estimator. This method provides accurate inference of an unknown covariance in non-standard settings, including heavy-tailed distributions and outlier contaminated scenarios. We begin with a survey of the estimator and its various derivations in the classical unconstrained settings. The latter rely on the theory of g-convex analysis which we briefly review. Building on this background, we enhance robust covariance estimation via g-convex regularization, and allow accurate inference using a smaller number of samples. We consider shrinkage, diagonal loading, and prior knowledge in the form of symmetry and Kronecker structures. We introduce these concepts to the world of robust covariance estimation, and demonstrate how to exploit them in a computationally and statistically efficient manner.
UR - http://www.scopus.com/inward/record.url?scp=84973667638&partnerID=8YFLogxK
U2 - 10.1561/2000000053
DO - 10.1561/2000000053
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AN - SCOPUS:84973667638
SN - 1932-8346
VL - 8
SP - 127
EP - 216
JO - Foundations and Trends in Signal Processing
JF - Foundations and Trends in Signal Processing
IS - 3
ER -