Score / rank covariance estimates

from precise import all_assessors, assessor_from_name

for A in all_assessors():
    s = A().score(cov, X_test=X_test, true_cov=Sigma_true)   # higher = better

• cov is the estimate to judge; X_test is held-out data (rows = observations); true_cov is the
  population covariance (only available in simulation).
• Each assessor exposes needs_data and needs_truth; pass what it needs. Truth-free assessors work on
  real data, truth-requiring ones (e.g. FrobeniusToTruth) only in simulation.
• All assessors follow higher = better, so you can rank or argmax directly.

The one rule that matters in high dimensions

Do not rank estimators by the held-out Gaussian log-likelihood when p is comparable to n. The
likelihood is dominated by the smallest, unidentifiable eigenvalues of the estimate; empirically it ranks
estimators below chance in that regime. Instead use inversion-free or block judges:

SchurLikelihood(gamma=...) is a tunable bridge: gamma=1 is the full likelihood (fragile in high-d),
gamma=0 the robust block-diagonal one, interior values better-conditioned than either.

Don't over-read the numbers

• Rankings are ensemble-sensitive: a result on one data-generating process need not transfer. If the
  conclusion matters, sweep several generators and report per-regime (see the
  assess-covariance-method skill).
• A lower point error (RMSE) is not a tradable or actionable signal by itself.
• If you attach significance to a ranking, the loss differentials are usually dependent (overlapping
  windows, correlated assets); naive standard errors overstate significance — see the inference section of
  the assess-covariance-method skill.