Bibliographic record
Abstract
In the problem of estimating bounded normal means, some improved lower bounds for the minimax quadratic risk are presented. Since these bounds hold for any sample size, not merely asymptotically, we refer to them as “nonasymptotic”. First, we will review and compare some well-known bounds due to van Trees, Chentsov, Bhattacharyya, Kooks, Casella-Strawderman, Ibragimov-Khasminskii, and Donoho. The goal is to obtain a reliable nonasymptotic lower bound for the minimax risk applicable to any sample sizes and — through the well-known method of the hardest one-dimensional subfamily — to related nonparametric estimation problems. A combined lower bound will be proposed and compared to the numerically evaluated minimax risk. This comparison shows that the proposed global bound is about 97% accurate for any sample sizes. The results will be applied to nonparametric estimation of linear functionals in the white Gaussian noise in Part II.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.035 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".