Closed odunbar closed 1 year ago
Other more recent shrinkage estimators (e.g. increased convergence due to Gaussian assumption) could also help?
Initial testing on branch orad/sec-ledwol
Naive implementation applying the shrinkage estimator to the samples [u;g]
leads almost always to shrinkage to the diagonal of C (i.e. [diag(C^uu) , diag(C^GG)
for ensemble sizes even near to parameter dimension.) I.e it does not work well for smaller ensembles.
I think due to the augmented state in EKP, the cross-covariance C^uG
is the important matrix candidate for localization/correction. Shrinkage however corrects the full covariance matrix C
. It also does not make sense to try to shrink C^uG
to any type of diagonal, as there is no reason for u_i
and G(u)_i
to be related.
Ledoit and Wolf 2004
, have a nice parameter-free covariance shrinkage estimator.Applied to the ensemble covariance, this could be an additional way to perform localization/sampling error correction in EKP in a principled way with no additional user parameters.
Implementation
Here is a snippet, which also removes the sample mean with Bessel correction.
sample_mat
is a matrix of samples of the covariance matrix stored as columns.