U-Statistics and Its Asymptotic Results for Some Inequality and Poverty Measures
Bibliographic record
Abstract
The U-statistics as a unique framework for a cluster of statistics is suitable to some income inequality and poverty measures. For ex-ample, the variance, Gini index or coefficient, poverty rate, poverty gap ratios, Foster-Greer-Thorbecke index, Sen index, and modified Sen index are good candidates because their sample counterparts can be viewed as either U-statistics themselves or functions of simpler U-statistics. This paper applies the existing theories for U-statistics to these suitable income inequality and poverty measures so that a gen-1 eral framework of statistical inference can be established. In particu-lar, with this framework, the asymptotic distributions of the sample Sen and modified Sen indices can be established. Acknowledgment: I wish to thank Yulia Kotlyarova, Stéphane Mussard and participants at the Statistics Colloquium, Department of Mathematics and Statistics, Dalhousie University, for helpful comments. Comments are welcome. 2 1
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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 | 0.021 | 0.115 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.002 | 0.007 |
| Scholarly communication | 0.003 | 0.010 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.009 |
| 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".