Asymptotic Distribution of Cramer-von Mises Statistic When Contamination Exists
Bibliographic record
Abstract
In this paper, asymptotic distribution of Cram\'er-von Mises goodness-of-fit test statistic is investigated when contamination exists. We first derive the asymptotic distribution of the Cram\'er-von Mises statistic when the observations are contaminated with noise as a mixture. The result is extended to the case where the parameters are estimated by the minimum distance estimator, which minimizes the Cram\'er-von Mises statistic. In both cases the asymptotic distribution of the Cram\'er-von Mises statistic is given by that of the weighted infinite sum of non-central $\chi^2_1$ variables and the effect of contamination appears only in the non-centrality of the variables. We also demonstrate the robustness of the goodness-of-fit test by Monte Carlo simulations when the parameters are estimated by the minimum distance estimator and the maximum likelihood estimator. Numerical experiments indicate that the use of the minimum distance estimator makes the test insensitive to contamination whereas the power is retained almost the same as that of the maximum likelihood estimator.
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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 | 0.018 | 0.165 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.002 | 0.007 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".