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Mayer Aladjem Publications

Multi-Target Shrinkage Estimation for Covariance Matrices

26 October, 2014

Authors: Tomer Lancewicki & Mayer Aladjem
Source: IEEE Transactions on Signal Processing (2014 in press)

Abstract: Covariance matrix estimation is problematic when the number of samples
is relatively small compared with the number of variables. One way to tackle
this problem is through the use of shrinkage estimators that offer a compromise
between the sample covariance matrix and a well-conditioned matrix (also
known as the "target") with the aim of minimizing the mean-squared
error (MSE). The use of only one target limits the shrinkage estimators' flexibility
when minimizing the MSE. In this paper, we propose a multi-target shrinkage
estimator (MTSE) for covariance matrices that exploits the Lediot-Wolf (LW)
method by utilizing several targets simultaneously. This greatly increases the
estimator's flexibility and enables it to attain a lower MSE. We also offer a
general target that serves as a framework for designing a wide variety of targets.
In consequence, instead of studying individual targets, the general framework
can be utilized. We then show that the framework encompasses several targets
that already exist in the literature. Numerical simulations demonstrate that
the MTSE significantly reduces the MSE and is highly effective in
classification tasks.