Comparisons of the Performances of Estimators of a Bounded Normal Mean Under Squared-Error Loss
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Bibliographic record
Abstract
This paper is concerned with the estimation under squared-error loss of a normal mean θ based on X ∼ N (θ, 1) when |θ| ≤ m for a known m > 0. Nine estimators are compared, namely the maximum likelihood estimator (mle), three dominators of the mle obtained from Moors, from Charras and from Charras and van Eeden, two minimax estimators from Casella and Strawderman, a Bayes estimator of Marchand and Perron, the Pitman estimator and Bickel’s asymptotically-minimax estimator. The comparisons are based on analytical as well as on graphical results concerning their risk functions. In particular, we comment on their gain in accuracy from using the restriction, as well as on their robustness with respect to misspecification of m.
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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