Structured robust covariance estimation

Ami Wiesel, Teng Zhang

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

Abstract

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.

Original languageAmerican English
Pages (from-to)127-216
Number of pages90
JournalFoundations and Trends in Signal Processing
Volume8
Issue number3
DOIs
StatePublished - 2014

Bibliographical note

Publisher Copyright:
© 2015 A. Wiesel and T. Zhang.

Cite this