Improving on the empirical covariance matrix using truncated PCA with   white noise residuals
  The empirical covariance matrix is not necessarily the best estimator for the population covariance matrix: we describe a simple method which gives better estimates in two examples. The method models the covariance matrix using truncated PCA with white noise residuals. Jack-knife cross-validation is used to find the truncation that maximises the out-of-sample likelihood score. 
Stephen Jewson