Uniformly Minimum Variance Unbiased Estimators (UMVUE) Not Attaining Cramer-Rao Lower Bounds
Bibliographic record
Abstract
The main thrust of this article is to provide counterexamples where the variance of the UMVUE does not achieve the Cramer-Rao lower bound. We provided many motivating counterexamples and showed that these UMVU estimators are, in fact, asymptotically efficient estimators. All counterexamples are new or may not be available in standard textbooks. To illustrate the entire process, we supplied many definitions related to UMVUE and described various methods and step-by-step approaches for finding UMVUE’s. In concluding remarks, we also gave a short biography of Professor C.R. Rao. It is hoped that the article will have pedagogical value in courses on statistical inference. IJSS, Vol. 24(2) Special, December, 2024, pp 1-18
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How this classification was reachedexpand
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 | 0.002 | 0.009 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".