Independent, Tough Identical Results: The Class of Tweedie on Power Variance Functions and the Class of Bar-Lev and Enis on Reproducible Natural Exponential Families
Bibliographic record
Abstract
The Rao-Blackwell theorem has had a fundamental role in statistical theory. However, as opposed to what seems natural, Rao and Blackwell did not investigate and write the theorem jointly. In fact, they both published the same result independently, two years apart. Indeed, as C.R. Rao writes in Wikipedia: ”the result on one parameter case was published by Rao (1945) in the Bulletin of the Calcutta Mathematical Society and by Blackwell (1947) in The Annals of Mathematical Statistics. Only Lehmann and Sche ´e (1950) called the result as Rao-Blackwell theorem”. Forty years later, a situation very similar to the previous one seems to have happened. Tweedie (1984) in a paper published in a proceedings to a conference held in Calcutta and Bar-Lev and Enis (1986) in a paper published in The Annals of Statistics both presented for the first time, albeit two years apart, independently and in di erent contexts, the class of natural exponential families having power variance functions (NEF-PVFs). Tweedie’s results were then mentioned by Jorgensen (1987) in his fundamental paper on exponential dispersion models published in the Journal of the Royal Statistical Society, Series B. Jorgensen, however, mentioned also other researchers, including Bar-Lev and Enis, as dealt with the same problem. Nonetheless, Jorgensen (1987) stated in his paper that ”The most complete study” of NEF-PVFs was given by Tweedie (1984), a statement which has led to naming the class of NEF-PVFs as the Tweedie class. This statement of Jorgensen is entirely and utterly incorrect. Accordingly, one of the goals of this note is to 'prove' such incorrectness. Based on this 'proof' it will be evident, so I trust, that both Bar-Lev and Enis should have received the appropriate credit by re-naming the class of NEF-PVFs via the exploitation of the names of Tweedie, Bar-Lev and Enis. This would resemble the dignified and elegant manner Lehmann and Sche ´e acted on the Rao-Blackwell Theorem. Notwithstanding, the main aim of the note is to encourage young researchers to present their results with self-confidence and to get the credit they deserve.
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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 | 0.083 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.007 | 0.005 |
| Science and technology studies | 0.005 | 0.012 |
| Scholarly communication | 0.010 | 0.024 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.005 | 0.012 |
| Insufficient payload (model declined to judge) | 0.012 | 0.004 |
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".