  Shrinkage can effectively improve the condition number and accuracy of
covariance matrix estimation, especially for low-sample-support applications
with the number of training samples smaller than the dimensionality. This paper
investigates parameter choice for linear shrinkage estimators. We propose
data-driven, leave-one-out cross-validation (LOOCV) methods for automatically
choosing the shrinkage coefficients, aiming to minimize the Frobenius norm of
the estimation error. A quadratic loss is used as the prediction error for
LOOCV. The resulting solutions can be found analytically or by solving
optimization problems of small sizes and thus have low complexities. Our
proposed methods are compared with various existing techniques. We show that
the LOOCV method achieves near-oracle performance for shrinkage designs using
sample covariance matrix (SCM) and several typical shrinkage targets.
Furthermore, the LOOCV method provides low-complexity solutions for estimators
that use general shrinkage targets, multiple targets, and/or ordinary least
squares (OLS)-based covariance matrix estimation. We also show applications of
our proposed techniques to several different problems in array signal
processing.
