Large covariance matrix estimation: Bridging shrinkage and tapering approaches
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Bibliographic record
Abstract
In this paper, we propose a shrinkage-to-tapering oracle (STO) estimator for estimation of large covariance matrix when the number of samples is substantially fewer than the number of variables, by combining the strength from both Steinian-type shrinkage and tapering estimators. Our contributions include: (i) Deriving the Frobenius risk and a lower bound for the spectral risk of an MMSE shrinkage estimator; (ii) Deriving a closed-form expression for the optimal coefficient of the proposed STO estimator. Simulations on auto-regression (e.g. a sparse case) and fraction Brownian motion (e.g. a non-sparse case) covariance structures are used to demonstrate the superiority of the proposed estimator.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it