Moments estimators and omnibus chi-square tests for some usual probability laws
Bibliographic record
Abstract
For many probability laws, in parametric models, the estimation of the parameters can be done in the frame of the maximum likelihood method, or in the frame of moment estimation methods, or by using the plug-in method, etc. Usually, for estimating more than one parameter, the same frame is used. We focus on the moment estimation method in this paper. We use the instrumental tool of the functional empirical process (fep) in Lo (2016) to show how it is practical to derive, almost algebraically, the joint distribution Gaussian law and to derive omnibus chi-square asymptotic laws from it. We choose four distributions to illustrate the method (Gamma law, beta law, Uniform law and Fisher law) and completely describe the asymptotic laws of the moment estimators whenever possible. Simulations studies are performed to investigate for each case the smallest sizes for which the obtained statistical tests are recommendable. Generally, the omnibus chi-square test proposed here work fine with sample sizes around fifty.
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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 | 0.038 | 0.260 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".