Semiparametric inference for the dominance index under the density ratio model
Bibliographic record
Abstract
An important and often discussed research problem in statistics is how to compare several populations; examples arise in medical science, engineering, finance and other fields. Often population means or medians are compared. However, one population may have a higher mean income, for example, because of a small number of super-rich individuals; the mean therefore may not reflect the wealth of the general population. Instead, an index of the degree of stochastic dominance of one population over another would better reflect their relative wealth. Currently, we can estimate such an index under restrictive conditions, but there is no generic estimator with a known asymptotic distribution. In this paper, we suggest linking the populations via the density ratio model. Under this model, we develop an empirical likelihood estimator and establish its asymptotic normality. In addition, we improve the estimation efficiency by examining the similarities between the populations. Furthermore, we provide a valid bootstrap method for hypothesis testing and the construction of confidence intervals. Simulation experiments show that the proposed estimator substantially improves the estimation efficiency and power of the test, and leads to confidence intervals with satisfactorily precise coverage probabilities. It is also robust with respect to mild model misspecification. Two examples are given to demonstrate the usefulness of both the method and the concept.
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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 | 0.017 | 0.087 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".