Tests for the first‐order stochastic dominance
Bibliographic record
Abstract
Abstract We study the first‐order stochastic dominance (SD) test in the context of two independent random samples. We introduce several test statistics that effectively capture violations of the dominance relationship, particularly in the tail regions. Additionally, we develop a resampling procedure to compute the ‐values or critical values for these tests. The proposed tests have asymptotic type I error rates for frontal configurations equal to the nominal level . Furthermore, their powers approach 1 for any fixed alternatives. Through simulation experiments, we demonstrate that our SD tests outperform the recentring test proposed by Donald and Hsu (2016) as well as the integral‐type test presented by Linton et al. (2010) in various scenarios discussed in existing literature. We also employ the proposed tests to analyze changes in the distribution of household income in the United Kingdom over time. The proposed tests offer some insights into potential dominance relationships within this context.
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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 | 0.041 | 0.290 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| 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".