Choosing the diagonal loading factor for linear signal estimation using cross validation

Linear signal estimation based on sample covariance matrices (SCMs) can perform poorly if the training data are limited and the SCMs are ill-conditioned. Diagonal loading (DL) may be used to improve robustness in the face of limited training data. This paper introduces two leave-one-out cross-validation schemes for choosing the DL factor. One scheme repeatedly splits the training data with respect to time, while the other repeatedly splits the out-of-training data with respect to space. We derive computationally efficient implementations and compare them with the oracle choice in terms of the mean squared error.