| name | score-covariance-estimate |
| description | Score and compare covariance estimates with precise's assessor panel. Use when you need to judge an estimate out-of-sample or rank competing estimators — and especially in high dimensions, where the plain held-out likelihood is misleading. |
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)
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:
| Regime / goal | Use |
|---|
| low dimension, well-conditioned | LogLikelihood (it is optimal here) |
high dimension (p/n near 1 or larger) | BlockPseudoLikelihood, SchurLikelihood, VariogramScore, FrobeniusToTruth (sim only) |
| economic / portfolio relevance | GMVVariance (out-of-sample minimum-variance variance) |
| forecasting a variance from a noisy proxy | a QLIKE / Bregman-consistent loss, not RMSE on the proxy — RMSE on a noisy variance proxy can rank inconsistently |
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.
