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.